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The impact of web-based assessment and practice on students' mathematics learning attitudes.



This study investigates the effects of web-based assessment and practice on improving middle school students' mathematics learning attitudes. With the use of an experimental design and a combination of quantitative and qualitative methods, the study compared and contrasted the attitude achievement of students, who used the web-based assessment and practice (WP) with students, who used the traditional assessment and practice (TP). Across multivariate The use of multiple variables in a forecasting model.  and factor analyses Verb 1. factor analyse - to perform a factor analysis of correlational data
factor analyze

analyse, analyze - break down into components or essential features; "analyze today's financial market"
 and the transcripts of interview notes, results of the study indicate that with the opportunities of drilling and practicing on the computer and receiving instant scores and adapted feedback, students had gained interests in doing mathematics, and formed a perception that they became smarter in problem-solving problem-solving nresolución f de problemas;
problem-solving skills → técnicas de resolución de problemas

problem-solving n
. However, the attitude improvements were quite different across ethnic and gender groups. Within the WP group, while male students gained more confidence than females, females expressed stronger opinions on the fact that instant scores and feedback helped them overcome difficulties in mathematics problem solving problem solving

Process involved in finding a solution to a problem. Many animals routinely solve problems of locomotion, food finding, and shelter through trial and error.
. Though some limitations still exist with written explanations and partial credits, in comparison with the traditional assessment, the web-based assessment and practice tool in this study substantially helps students build motivation and elevates the meaning of learning and doing mathematics with the use web-based technology.

**********

One of the important components in the growth and evolution of mathematics teaching and learning is the emergence of web-based technologies. The uses of innovative web-based technology, especially in the assessment, enhance students' activities in mathematics learning when the web-based assessment engine is well designed and appropriately and timely used (King, 1997). Furthermore, with a broad implementation of online instructional materials along with the need of improving large-scale large-scale
adj.
1. Large in scope or extent.

2. Drawn or made large to show detail.


large-scale
Adjective

1. wide-ranging or extensive

2.
 state and national testing, the integration of innovative web-based technology in improving assessment becomes the main focus of the education in all subjects. According to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 Bennett (2001), web-based assessment can be considered as "interactive, broadband broadband

Term describing the radiation from a source that produces a broad, continuous spectrum of frequencies (contrasted with a laser, which produces a single frequency or very narrow range of frequencies).
, networked, and standard-based" instrument. Web-based delivery assessment affords a large number of randomized ran·dom·ize  
tr.v. ran·dom·ized, ran·dom·iz·ing, ran·dom·iz·es
To make random in arrangement, especially in order to control the variables in an experiment.
 items with immediate scoring and feedback, a rapid return of large number of tests and survey results (Linn linn  
n. Scots
1. A waterfall.

2. A steep ravine.



[Scottish Gaelic linne, pool, waterfall.]
, 2002; Bennett, 2001), and an automatic diagnosis system for performance evaluation Performance evaluation

The assessment of a manager's results, which involves, first, determining whether the money manager added value by outperforming the established benchmark (performance measurement) and, second, determining how the money manager achieved the calculated return
 (Nguyen & Kulm Kulm: see Chełmno, Poland. , 2005). Recently, with the emergence of Java, JavaScript JavaScript

Computer programming language developed by Netscape in 1995 for use in HTML pages. JavaScript is a scripting language (or interpreted language), which is not as fast as compiled languages (such as Java or C++) but easier to learn and use.
, Mathlets, and HTML HTML
 in full HyperText Markup Language

Markup language derived from SGML that is used to prepare hypertext documents. Relatively easy for nonprogrammers to master, HTML is the language used for documents on the World Wide Web.
, web-based assessment has become interactive medium for delivering both instruction and assessment in mathematics (Sanchis, 2001).

Web-based assessment provides students with more chances for practice, self-testing, self-regulation The term self-regulation can signify
  • in systems theory: homeostasis
  • in sociology / psychology: self-control
  • in educational psychology: self-regulated learning
  • Self-Regulation Theory (SRT) is a system of conscious personal health management
, and self-evaluation, while teachers receive more feedback from students, save time in reading and grading, and have closer interactions with students (Fleischman, 2001; Lockwood Lock·wood   , Belva Ann Bennett 1830-1917.

American lawyer and suffragist. She was the first woman admitted to practice before the U.S. Supreme Court (1879).
, 2001). In using a web-based assessment tool, teachers can integrate the different content areas for their students and enhance students' attitude and motivation toward the learning subject. At the same time, students can use online technology in learning and helping themselves succeed (Morgan Morgan, American family of financiers and philanthropists.

Junius Spencer Morgan, 1813–90, b. West Springfield, Mass., prospered at investment banking.
 & O'Reilly, 2001).

PURPOSE OF THE STUDY AND RESEARCH QUESTIONS

Upon recent suggestions of the use of web-based assessment in enhancing mathematics teaching and learning, this study profoundly discovered the effects of web-based assessment and practice on students' mathematics learning attitudes. Explicating unique capabilities of the innovative online practice on making crucial contributions to the traditional practice would lead to suggestions for future use and appropriate development of online mathematics assessment and tutorial system At both University of Cambridge and University of Oxford, undergraduates are taught in the tutorial system. Students are taught by faculty fellows in groups of one to three. At Cambridge, these are called "supervisions" and at Oxford they are called "tutorials. . The comparisons of online and traditional paper-and-pencil practices were conducted to determine the effective and relevant components of online delivery medium. The research mainly investigated: (a) the effect of web-based assessment and practice on middle graders mathematics learning attitudes; and (b) the mathematics learning attitudes among students in the web-based group in terms of genders and different ethnicities.

THEORETICAL BACKGROUND

Emergence of Web-Based Technology in Teaching and Learning

The recommendations of the congressional Web-Based Education Commission (WBEC WBEC Web Based Education Commission , 2001) make a compelling case for integrating and making use of the web-based applications See Web application.  in classrooms. Morgan and O'Reilly (2001) have reported that online technologies have significantly increased the opportunities for innovative assessments. These innovative assessments push the boundary of the traditional paper-based learning experience with current online technology. In the recent time, web-based instruction and web-based drill-and-practice have commonly served as tutorials in the educational setting (Nguyen & Allen Al·len , Edgar 1892-1943.

American anatomist who is noted for his studies of hormones and for the discovery (1923) of estrogen.
, 2006). Merill and Hammons (1996) indicated that these tutorials can fill the gaps and reinforce concept learning by presenting alternative methods, checking for understanding, providing explanations when appropriate, and indicating mastery level of computational Having to do with calculations. Something that is "highly computational" requires a large number of calculations.  skills. Tutorial An instructional book or program that takes the user through a prescribed sequence of steps in order to learn a product. Contrast with documentation, which, although instructional, tends to group features and functions by category. See tutorials in this publication.  uses can effectively provide students with controls over their learning (Sanchis, 2001). Free access to web-based lesson planning and online tutorials, such as the Math Forum, Compass, SOS SOS, code letters of the international distress signal. The signal is expressed in International Morse code as … — — — … (three dots, three dashes, three dots). , and many other state resources offer students tremendous information to improve their learning. At the same time, students can engage in meaningful learning rather than memorization mem·o·rize  
tr.v. mem·o·rized, mem·o·riz·ing, mem·o·riz·es
1. To commit to memory; learn by heart.

2. Computer Science To store in memory:
 to develop their own interest toward mathematics learning.

WEB-BASED DRILL AND PRACTICE ENHANCING MATHEMATICS LEARNING ATTITUDE AND ACHIEVEMENT

According to Hart and Walker (1993), students' attitudes toward a learning subject vary based on characteristics of classroom and instruction, such as types of assessment, topics, and material delivery tools. Steele and Arth ARTH Arabidopsis Thaliana  (1998) also indicated that the flexibility about accepting students' ways of solving problems can increase students' participation, reduce anxiety, and increase positive attitudes in learning. Web-based applications can create different learning and assessment contexts, and produce flexible approaches to instruction and evaluation (Allen, 2001; Liang Liang  

The name of two Chinese dynasties, the Earlier Liang Dynasty (502-557) and the Later Liang Dynasty (907-923).
 & Creasy crease  
n.
1. A line made by pressing, folding, or wrinkling.

2. Sports
a. A rectangular area marked off in front of the goal in hockey and lacrosse.

b.
, 2004). Assessment that is provided on the web-based medium allows students to have more control over their practice and to receive reinforcement reinforcement /re·in·force·ment/ (-in-fors´ment) in behavioral science, the presentation of a stimulus following a response that increases the frequency of subsequent responses, whether positive to desirable events, or  that can help them to build intrinsic intrinsic /in·trin·sic/ (in-trin´sik) situated entirely within or pertaining exclusively to a part.

in·trin·sic
adj.
1. Of or relating to the essential nature of a thing.

2.
 motivation and improve their confidence (Middleton Middleton, city (1991 pop. 51,373), Rochdale metropolitan district, NW England, in the Greater Manchester metropolitan area on the Irk River. Manufactures include cotton, silks, chemicals, plastics, and soap.  & Spanias, 1999; Nguyen & Kulm, 2005).

Several studies have shown that students who used computer-based learning practice find mathematics more enjoyable. They like the flexible features provided by the computer practice, spend long hours at a computer to complete a task, and enjoy testing out new ideas "New Ideas" is the debut single by Scottish New Wave/Indie Rock act The Dykeenies. It was first released as a Double A-side with "Will It Happen Tonight?" on July 17, 2006. The band also recorded a video for the track.  on a computer (Galbraith Gal·braith   , John Kenneth Born 1908.

Canadian-born American economist, writer, and diplomat who served as U.S. ambassador to India (1961-1963). His works include The Great Crash (1955).

Noun 1.
 & Haines Haines refers to: Persons named Haines
  • Avery Haines (1966–), Canadian television journalist
  • Daniel Haines (1801–1877), American jurist and governor of New Jersey
  • Donald Haines (1918–1941), American child actor (Our Gang)
, 1998; Anderson Anderson, river, Canada
Anderson, river, c.465 mi (750 km) long, rising in several lakes in N central Northwest Territories, Canada. It meanders north and west before receiving the Carnwath River and flowing north to Liverpool Bay, an arm of the Arctic
, 1995; Chi, Lewis, Reiman, & Glaser Noun 1. Glaser - United States physicist who invented the bubble chamber to study subatomic particles (born in 1926)
Donald Arthur Glaser, Donald Glaser
, 1989; Reif n. 1. Robbery; spoil. , 1987). Galbraith and Haines (1998), and Pemberton People
  • Brock Pemberton (1885-1950), U.S. theatrical producer and director
  • Caroline Pemberton (born 1986), Australian model
  • Charley Pemberton (1854-1894), son of John Pemberton
  • John Pemberton (1831-1888), inventor of Coca-Cola
  • John C.
 (1996) agreed that computer and web-based applications increased students' level of confidence, motivation, engagement, and interaction.

Web-based assessment has the potential to meet the authentic assessment Authentic assessment is an umbrella concept that refers to the measurement of "intellectual accomplishments that are worthwhile, significant, and meaningful,"[1] as compared to multiple choice standardized tests.  standards defined by Kulm (1994). Those authentic assessment tasks can serve the following objectives: (a) improvement of instruction and learning; (b) feedback for the students, providing information to aid them in seeing inappropriate strategies, thinking, or habits; and (c) improvement of attitudes toward mathematics (Kulm, 1994, p. 4). Previous research on the integration of web-based technology into mathematics teaching and learning has shown promising and positive effects. The web-based technology is emerging as one of the best media of user interface and instructional delivery and assessment. The web-based assessment, according to Allen (2001) constitutes an integral part of the curriculum and learning process.

Limitations of Web-Based Technology in Assessment

Despite its flexibility and portability, web-based instruction and assessment has some limitations. For example, students must have reliable access to computer and a connection to the Internet Internet

Publicly accessible computer network connecting many smaller networks from around the world. It grew out of a U.S. Defense Department program called ARPANET (Advanced Research Projects Agency Network), established in 1969 with connections between computers at the
 without time restrictions. Some technical problems, such as slow modem speed, slow bandwidth, or network jam may need to be allowed for the use of the web-based tool. The web-based assessment does not provide partial credits and does not sufficiently grade all mathematical equivalent forms of short answers. Research by Russell Russell, English noble family. It first appeared prominently in the reign of Henry VIII when

John Russell, 1st earl of Bedford, 1486?–1555, rose to military and diplomatic importance.
 and Haney (1997) and Russell (1999) have shown that assessment presented by computer underestimated students' mathematics achievement regardless of their level of computer familiarity. However, the assessment tool used in Russell and Haney research was delivered through a network-based system with very little or almost no flexibility, and was simply a paper-and-pencil assessment that was transcribed into computer screen and without feedback. That was very different in comparison with the recent dynamic and interactive web-based assessment with the aid of Java, JavaScript, Mathlets, and HTML. Moreover, to meet the current demands of the technological era, web-based practice has continued to be developed, and has perpetually per·pet·u·al  
adj.
1. Lasting for eternity.

2. Continuing or lasting for an indefinitely long time.

3. Instituted to be in effect or have tenure for an unlimited duration:
 improved its unique features and characteristics. Furthermore, to meet the demands of National Council of Teachers of Mathematics The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally.  (NCTM NCTM National Council of Teachers of Mathematics
NCTM Nationally Certified Teacher of Music
NCTM North Carolina Transportation Museum
NCTM National Capital Trolley Museum
NCTM Nationally Certified in Therapeutic Massage
) (2000) in using assessment to improve mathematics achievement, there is a need for research to discover the development and implementation methods and the extraneous ex·tra·ne·ous  
adj.
1. Not constituting a vital element or part.

2. Inessential or unrelated to the topic or matter at hand; irrelevant. See Synonyms at irrelevant.

3.
 effects of web-based assessment on students' learning and achievement that paper-and-pencil assessment just cannot accomplish.

Methodology

This study applied a quasi-experimental design and combinations of quantitative and qualitative data collection and analyses. The instruments of the study contained four homework practice sets adapted from the Connected Mathematics series (Lappan, Fey, Fitzgerald, Friel Friel is a surname, and may refer to
  • Anna Friel, British actress
  • Brian Friel, Northern Ireland playwright and director
  • Courtney Friel, American television presenter
  • Henry J.
, & Phillips Phil·lips  

A trademark used for a screw with a head having two intersecting perpendicular slots and for a screwdriver with a tip shaped to fit into these slots.
, 1998) with randomized items and instant feedback, pre and post written surveys and interview questionnaires. Participants were 74 seventh graders, 44 males and 30 females, from a middle school in the Southern Texas. Students were from four class periods taught by the same mathematics teacher. The racial composition was 22% Hispanic Hispanic Multiculture A person of Mexican, Puerto Rican, Cuban, Central or South American, or other Spanish culture or origin, regardless of race Social medicine Any of 17 major Latino subcultures, concentrated in California, Texas, Chicago, Miam, NY, and elsewhere , 64% White, and 14% African American African American Multiculture A person having origins in any of the black racial groups of Africa. See Race. . They were randomly assigned as·sign  
tr.v. as·signed, as·sign·ing, as·signs
1. To set apart for a particular purpose; designate: assigned a day for the inspection.

2.
 to either the paper-and-pencil group (N=33, 44.6 %) or the web-based group (N=41, 55.4 %). Students in the web-based group (the WP group) worked with online practice tasks in their school computer lab during the math class periods. Students in the paper-and-pencil group (the TP group) worked with the conventional paper-and-pencil practice tasks in the traditional classroom with their mathematics teacher.

Chi-square tests chi-square test: see statistics.  were conducted for the comparisons among groups in terms of their gender, grade, and ethnicity ethnicity Vox populi Racial status–ie, African American, Asian, Caucasian, Hispanic . The results showed that there was no significant difference among the proportion of male and female students in both groups, [[[lambda].sup.2] (1, N = 74) = 0.597, p = .440]. Also, there existed no significant difference among the proportion of students with different grades in both groups, [[[lambda].sup.2] (1, N = 74) = 0.016, p = .898]. No significant difference was found among the proportion of students with different ethnicities in both groups, [[[lambda].sup.2] (2, N = 74) = 0.626, p = .73]. Further, chi-square tests also suggested that the two groups did not differ significantly for the variables of "whether have computers at home" [[[lambda].sup.2] (1, N = 74) = 1.317, p = .251], and "number of hours spends on computers each week" [[[lambda].sup.2] (3, N = 74) = 6.853, p = .077]. Insignificant statistical differences among the proportion of gender, grade, ethnicity, and computer using indicate that even though being randomly selected, the characteristics of the two groups were similar. With the presented evidence of groups' equivalence, it is thus appropriate for researchers to conduct comparisons between groups in terms of independent and dependent variables explored.

Instruments

Homework and practice tasks. Four online homework and practice sets were designed for this study. These sets included practice tasks on fractions and decimals with randomized items, automatic grading, and immediate adapted feedback. These items were selected from the Connected Mathematics series (Lappan et al., 1998), and were examined by six middle school teachers and the Principle Investigator of the National Science Foundation--Middle School Mathematics Project (MSMP MSMP Modeling & Simulation Master Plan (DoD 5000 59-P)
MSMP More Secure Mnemonic Password
MSMP Multi Service Muxponder
). These items were transcribed into a computer database, coded in the form of mathematical formulas with random parameters and conditional statements, and implemented into the web-based server by a mathematics educator who was also a member of the MSMP. The random parameters were chosen by selecting appropriate number range, word group, and/or and/or  
conj.
Used to indicate that either or both of the items connected by it are involved.

Usage Note: And/or is widely used in legal and business writing.
 size and shape type, depending upon each individual item. Before parsing See parse.

parsing - parser
 into the mathematical formula, the random parameters had also passed the conditional testing, basically the procedural testing with the combination of numbers, to assure the uniform level of difficulty for each generated item. The feedback was generated upon the preset preset Cardiac pacing A parameter of a pacemaker that is programmed permanently when manufactured  conditional statements. For adapted feedback to be generated, several predicted mistakes or errors for individual item were encoded in various mathematical categories along with suggestions, those were also in the form of mathematical formulas that took the parsing parameters, for correction. The practice tasks included both multiple-choice mul·ti·ple-choice
adj.
1. Offering several answers from which the correct one is to be chosen: a multiple-choice question.

2.
 and short-answer items regarding fraction operations, including addition, subtraction subtraction, fundamental operation of arithmetic; the inverse of addition. If a and b are real numbers (see number), then the number ab is that number (called the difference) which when added to b (the subtractor) equals , multiplication multiplication, fundamental operation in arithmetic and algebra. Multiplication by a whole number can be interpreted as successive addition. For example, a number N multiplied by 3 is N + N + N. , division and simplification, conversion of fractions and decimals, and word problems. Mathematical skills and concepts were combined and applied in the context of word problems. A variety of mathematical procedures and concepts were included to accommodate different features and mastery skills of each student. The homework and practice tasks were arranged into two parts. The first part was the review of fraction operations and fraction and decimal Meaning 10. The numbering system used by humans, which is based on 10 digits. In contrast, computers use binary numbers because it is easier to design electronic systems that can maintain two states rather than 10.  conversion techniques with brief reviews shown by tables, maps, charts, and worked out examples. The second part contained 15 multiple-choice and short-answer items. Each item was accompanied with detailed feedback and solution that could be seen if the students chose to check the answer after he/she clicked on grading the item. Figures 1, 2a, and 2b show a sample homework question and feedback.

Fill in the missing numbers in the fraction addition below:

[FIGURE 1 OMITTED]

[FIGURE 2A OMITTED]

[FIGURE 2B OMITTED]

Web-based system. Each student could access the online homework with his or her assigned password. While doing homework, the student could get extra help by scrolling (chat, games) scrolling - To flood a chat room or Internet game with text or macros in an attempt to annoy the occupants. This can often cause the chat room to be "uninhabitable" due to the "noise" created by the scroller. Compare spam.  back to the review section (the first part of the homework as described in the homework and practice tasks section), and either doing some practices or viewing the worked out examples. Though the student did receive the feedback for the practice, the practice problems while taking the homework would not be graded. Additionally, the online homework was customized so that the student did not have the permission to view the source code. Once the homework was submitted, the student received a summarized table that showed the total score, his or her answer for each question verses the correct answer, and a check mark that indicated correct or incorrect.

Survey questionnaires. Pre-and-postsurveys were designed to collect information regarding students' computer familiarity, attitude toward mathematics, attitude toward computer use, and attitude toward the online mathematic learning and practice.

The presurvey for both WP and TP groups consisted of 20 statements and was divided into two subcategories: (a) Attitude toward mathematics with 10 statements adapted from the Aiken Aiken, city (1990 pop. 19,872), seat of Aiken co., W S.C.; inc. 1835. A resort and polo center and a training area for Thoroughbreds, Aiken has apparel, printing and publishing, drug, and chemical industries.  Mathematics Attitude Scales (Aiken & Dreger, 1961) and the Revised Fennema-Sherman Attitude Scales (Fennema & Sherman Sherman, city (1990 pop. 31,601), seat of Grayson co., N Tex., near the Red River; inc. 1858. Originally on a stagecoach route, it is a highway and railroad junction. Manufactures include electronic equipment, processed foods, military equipment, and metal products. , 1976) aimed at measuring students' self-perception self-per·cep·tion
n.
An awareness of the characteristics that constitute one's self; self-knowledge.
 in mathematics learning, and their motivation and interests in mathematics problem solving; and (b) Attitude toward computer usage with 10 statements adapted from the Instrument for Assessing Educator Progress in Technology Integration from the University of North Texas, aimed at checking students' level of interests and familiarity in computer use (Knezek, Rhonda, Miyashita, & Ropp, 2002). A 5-point Likert scale Likert scale A subjective scoring system that allows a person being surveyed to quantify likes and preferences on a 5-point scale, with 1 being the least important, relevant, interesting, most ho-hum, or other, and 5 being most excellent, yeehah important, etc  ranging from strongly agree-5, agree-4, netural-3, disagree-2; strongly disagree-1 was used to record students' responses.

The postsurvey for the TP group included 10 statements, excerpted from the first subcategory sub·cat·e·go·ry  
n. pl. sub·cat·e·go·ries
A subdivision that has common differentiating characteristics within a larger category.
 in the presurvey questionnaire, which checked students' postattitude toward mathematics. The postsurvey for the WP group contained 25 statement questions: (a) 10 statements, that were identical with the statements for the TP group, aimed at measuring students' postattitude toward mathematics; and (b) 15 statements to capture students' postattitude toward online mathematic learning and practice, which focused on eliciting participants' evaluation, perceptions and opinions regarding the effects of web-based mathematics assessment, scoring, feedback and practice features on their learning.

Interviews. There were 10-minute face-to-face (jargon, chat) face-to-face - (F2F, IRL) Used to describe personal interaction in real life as opposed to via some digital or electronic communications medium.  interviews with 12 selected students from the WP group on the last day of the study. These 12 students were randomly selected from different gender and ethnic groups to assure the collection of diverse opinions. The purpose of the interview was to further explore the effects of online assessment on students' attitude and motivation. The interview questions were an oral repeat of the postsurvey statements to probe areas that might be practically difficult for students to articulate articulate /ar·tic·u·late/ (ahr-tik´u-lat)
1. to pronounce clearly and distinctly.

2. to make speech sounds by manipulation of the vocal organs.

3. to express in coherent verbal form.

4.
 in the written form.

Procedures

Students participated in this study 30 minutes each day and three times a week. The study lasted for three weeks. Prior to the study, all students were asked to complete the presurvey. During the study, both WP and TP groups practiced four different sets of homework as described in the homework and practice tasks section. The WP group practiced the homework in the computer lab. They had an option to check if they got the correct or incorrect answer for each question. They also received immediate feedback for each incorrect answer and the total score when they finished each homework set. Because of the random feature, students were allowed to practice as many times as they wished. These students were informed that the highest practice score would be recorded and reported to the teacher. Every time students repeated each homework set, the homework items were slightly changed by the random parameters, such as numbers, words, or choices, but the mathematics content and concept remained the same.

The TP group practiced the same homework sets as the WP group, but on printed worksheets. There were two alternative versions of each printed homework task available. Students in the TP group were encouraged (but not required) to take these alternative ones for extra practice. If students had questions, they could get help from their teacher. The students' homework papers were collected, manually graded, and returned to students by their teacher. At the end of the study, the WP and TP groups both took the mathematics postsurvey.

DATA ANALYSES

Prior to the factor analysis of the entries in the presurvey questionnaire, the Kaiser-Meyer-Olkin Measure of Sampling Adequacy Test was used to examine whether the distribution of values was adequate for conducting factor analysis. In this case, the Kaiser designated 0.798, indicating it was middling and acceptable for factor analysis. Also, the Bartlett's Test Bartlett's test (Snedecor and Cochran, 1983) is used to test if k samples have equal variances. Equal variances across samples is called homoscedasticity or homogeneity of variances.  of Sphericity presented a significant value (p< .05), meaning that these data did not produce an identity matrix and were thus approximately multivariate normal and acceptable for factor analysis.

Similarly, the Kaiser-Meyer-Olkin Measure of Sampling Adequacy Test was performed to examine whether the distribution of values in the postsurvey questions was adequate for conducting factor analysis. It turned out that the Kaiser was 0.702; the Bartlett's Test of Sphericity also generated a significant value (p< .05), indicating that these data were nearly multivariate normal and acceptable for factor analysis.

Accordingly, exploratory factor analyses were performed on the 10 items of the Attitude toward Mathematics Scale, 10 items of the Attitude toward Computer Usage, and 15 items of the Attitude toward Web-Based Mathematic Learning and Practice, based on the principal axis Noun 1. principal axis - a line that passes through the center of curvature of a lens so that light is neither reflected nor refracted; "in a normal eye the optic axis is the direction in which objects are seen most distinctly"
optic axis
 technique with a varimax rotation (Norusis, 1986). Further, the following criteria: (a) computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking.  of the percentage of variance The discrepancy between what a party to a lawsuit alleges will be proved in pleadings and what the party actually proves at trial.

In Zoning law, an official permit to use property in a manner that departs from the way in which other property in the same locality
 extracted, and (b) performance of a Scree test (Comrey & Lee, 1992) were used to determine the optimum factor solution.

Descriptive statistics descriptive statistics

see statistics.
 were performed on all variables, including means and standard deviation In statistics, the average amount a number varies from the average number in a series of numbers.

(statistics) standard deviation - (SD) A measure of the range of values in a set of numbers.
. Prior to the study, a multivariate analysis multivariate analysis,
n a statistical approach used to evaluate multiple variables.

multivariate analysis,
n a set of techniques used when variation in several variables has to be studied simultaneously.
 of variance (MANOVA MANOVA Multivariate Analysis of the Variance ) was used to determine differences between the mean scores of attitudes toward mathematics learning and computer usage by group. After the treatment, MANOVA was conducted to determine differences between the mean scores of attitudes toward mathematics learning by group. For the WP group, a MANOVA was computed to determine the differences between the mean scores of students' attitudes toward online practice by gender and ethnicity (African American, Hispanic and White). The alpha level was set at 0.05. Data was analyzed an·a·lyze  
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.

2. Chemistry To make a chemical analysis of.

3.
 by using SPSS A statistical package from SPSS, Inc., Chicago (www.spss.com) that runs on PCs, most mainframes and minis and is used extensively in marketing research. It provides over 50 statistical processes, including regression analysis, correlation and analysis of variance.  11.0 for Windows.

In addition to the quantitative data analysis, the content analyses approaches, as described by Emerson, Fretz, and Shaw (1995), were applied to the researchers' journal entries and interview notes. During and upon completion of data collections, the two-phase two-phase
adj. Electricity
Relating to two alternating currents with phases differing by 90°.
 process of content analyses, open coding and focused coding, was used to analyze the data to profoundly explicate the effects of online practice on students' mathematics learning attitudes.

QUANTITATIVE RESULTS

Factor Analysis of Presurvey Questionnaire for all Participants

The presurvey questionnaire for both WP and TP groups originally consisted of 20 statements with 10 items on Attitude toward Mathematics, and another 10 items on Attitude toward Computer Usage. With the examination of results in factor analysis and reliability test, two inappropriate items were removed. In the end, the presurvey items consisted of 18 questions with 9 items on Attitude toward Mathematics, and another 9 items on Attitude toward Computer Usage.

The examination of the Scree plot and the eigenvalues eigenvalues

statistical term meaning latent root.
 depicted de·pict  
tr.v. de·pict·ed, de·pict·ing, de·picts
1. To represent in a picture or sculpture.

2. To represent in words; describe. See Synonyms at represent.
 three factors underlay the presurvey questionnaire. The first factor was associated with 30.78 % of the total common variance, the second with 19.44 % of the total variance before rotation, the third with 9.28 % of the total variance before rotation; these three factors together being associated with 59.50 % of the total common variance. Subsequent factors did not explain more than 5.5% of the total variance alone. Investigation of the rotated rotated

turned around; pivoted.


rotated tibia
see rotated tibia.
 factor loadings further revealed that items were weighted high on one of three factors: (a) the value of computer usage in learning, (b) positive affection of doing mathematics, and (c) the value of studying mathematics. Table 1 and Table 2 showed the component (factor) transformation matrix and rotated component matrix of the presurvey items.

Additionally, to validate To prove something to be sound or logical. Also to certify conformance to a standard. Contrast with "verify," which means to prove something to be correct.

For example, data entry validity checking determines whether the data make sense (numbers fall within a range, numeric data
 the reliability of the presurvey, coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 alpha for each factor was computed and gained the value of [alpha] to be 0.87, 0.85, and 0.74 respectively.

Factor Analysis of Postsurvey Questionnaire for the WP Group

The postsurvey questionnaire for the WP group originally contained 25 statements with 10 items on Attitude toward Mathematics, and 15 items in Attitude toward Web-Based Mathematic Learning and Assessment. With the examination of results in factor analysis and reliability test, six inappropriate items was removed. In the end, the postsurvey items consisted of 19 questions with 6 items on Attitude toward Mathematics, and 13 items on Attitude toward Web-Based Mathematic Learning and Assessment.

The examination of the scree plot and the eigenvalues depicted three factors underlay the postsurvey questionnaire. The first factor was associated with 43.23% of the total common variance, the second with 19.98% of the total variance before rotation, the third with 5.65% of the total variance before rotation; these three factors together being associated with 68.86% of the total common variance. Subsequent factors did not explain more than 5% of the total variance alone. Investigation of the rotated factor loadings further revealed that items were weighted high on one of three factors: (a) the general perception of learning math on computers, (b) positive affection of doing mathematics, and (c) the value of web-based mathematic instruction. Table 3 and Table 4 show the component (factor) transformation matrix and rotated component matrix of the postsurvey items for the WP group. Additionally, to validate the reliability of the presurvey, coefficient alpha for each factor was computed and gained the value of to be 0.93, 0.89 and 0.82, respectively.

GROUP COMPARISONS IN ATTITUDES TOWARD MATHEMATICS LEARNING AND COMPUTER USAGE

Prior to the Study

A multivariate analysis of variance (MANOVA) was computed to determine differences between the mean scores of attitudes toward mathematics learning and computer usage by group prior to the study. There was no significant difference between the WP and TP groups for the attitude variables in the presurvey (p value ranging from .065 to .965).

Group Comparisons in Attitudes toward Mathematics Learning After the Treatment

The descriptive statistics results showed that in the TP group, there were 15 (46%) females and 18 (54%) males, and 23 (70%) White, 6 (18%) Hispanic and 4 (12%) African American. In the WP group, there were 15 (37%) females and 26 (63%) males, and 25 (61%) White, 10 (24%) Hispanic and 6 (15%) African American. The multivariate analysis of variance (MANOVA) was conducted to determine differences between the mean scores of attitudes toward mathematics learning after the treatment. The results showed that there were no significant differences between groups, and no significant interaction between group and gender in the designated six dependent variables.

However, after the examination of the descriptive statistics, it was found that after the treatment while responding to the statement of "I am sure of myself when I do math," male students in the WP group (M=3.6, SD=0.21) yielded apparently higher scores than the males in the TP group (M=3.2, SD=0.25); yet, the WP group of female students' average rating score remained similar to the females in the TP group (M=3.2, SD=0.27).

Further, when responding to the statement of "I can do well in math," male students in the WP group (M=4.0, SD=0.19) yielded higher scores than the males in the TP group (M=3.7, SD=0.23); yet, the WP group of female students' average score showed lower score (M=3.6, SD=0.25) compared to the females in the TP group (M=3.8, SD=0.25).

Similarly, when asked to respond to the statement of "I think I could handle more difficult math," male students in the WP group (M=3.4, SD=0.23) yielded seemingly seem·ing  
adj.
Apparent; ostensible.

n.
Outward appearance; semblance.



seeming·ly adv.
 higher scores than the males in the TP group (M=2.83, SD=0.28); however, the WP group of female students' showed lower score (M=2.7, SD=0.31) compared to the females in the TP group (M=2.9, SD=0.31).

Concerning the statement of "I enjoy math problem solving," it was found that male students in the TP group (M=2.8, SD=0.28) yielded lower mean scores than the females in that group (M=3.1, SD=0.3). But in the WP group, male students (M=3.6, SD=0.23) had higher mean score than the females' (M=3.2, SD=0.3). Additionally, male students in the WP group (M=3.6, SD=0.23) yielded higher scores than the males in the TP group (M=2.8, SD=0.28); the WP group of female students' also showed higher score (M=3.3, SD=0.3) compared to the females in the TP group (M=3.1, SD=0.3).

Moreover, it was surprising to find that when asked to rate the statement of "I study math because I know how useful it is," males and females students in the WP group ([M.sub.male]=3.9, [SD.sub.male]=0.19; [M.sub.female]=3.7, [SD.sub.female]=0.25) both had lower mean scores than those in the TP group ([M.sub.male]=4.2, [SD.sub.male]=0.23; [M.sub.female]=3.8, [SD.sub.female]=0.25).

The WP Group' Attitudes Toward Web-Based Mathematic Learning and Assessment in Terms of Different Gender and Ethnicity

A multivariate analysis of variance (MANOVA) was computed to determine differences by gender and ethnicity for the 19 attitude variables shown in the postsurvey for the WP group after the treatment. The statistic statistic,
n a value or number that describes a series of quantitative observations or measures; a value calculated from a sample.


statistic

a numerical value calculated from a number of observations in order to summarize them.
 result showed that there was a significant interaction between gender and ethnicity (F(20, 17) = 2.741, p< .05) (Table 5). In tests between-subjects effects by gender and ethnicity, it was found that there was a significant main effect by ethnicity in the attitude toward the dependent variable "I am sure of myself when I do math."

Further, the post hoc post hoc  
adv. & adj.
In or of the form of an argument in which one event is asserted to be the cause of a later event simply by virtue of having happened earlier:
 tests indicated that White and Hispanic students had significant difference in rating the statement of "I am sure of myself when I do math." The mean score yielded by the White students was 3.16 (SD=1.03) whereas the Hispanic students produced a significantly higher score of 4.20 (SD=0.79). Another significant difference existed between the White and Hispanic students in the dependent variable of "I think I could handle more difficult math." The mean score yielded by the White students was 2.84 (SD=1.21); on the contrary, the Hispanic students had a higher mean score of 4.10 (SD=0.88).

There was also a significant univariate univariate adjective Determined, produced, or caused by only one variable  interaction of gender by ethnicity on the following dependent variables: "I like to receive immediate scores on my math homework and quizzes from the computer," "Computer immediate feedback is useful for mathematics problem solving," "I have less anxiety in taking computer-based quizzes than paper-and-pencil quizzes," and "Computer-based math quizzes with immediate scoring help me evaluate my own understanding and performance" (Table 6).

The descriptive statistical results indicated that when asked to measure their attitude toward the statement of "I like to receive immediate scores on my math homework and quizzes from the computer," White female students (M=4.92, SD=0.29) produced higher scores than the African American females (M=4.00, SD=1.73). Conversely con·verse 1  
intr.v. con·versed, con·vers·ing, con·vers·es
1. To engage in a spoken exchange of thoughts, ideas, or feelings; talk. See Synonyms at speak.

2.
, White male students (M=4.69, SD=0.63) yielded lower scores than the African American students (M=5.0, SD=0).

Moreover, when asked to rate their attitude toward the statement of "Computer immediate feedback is useful for mathematics problem solving," White female students (M=4.42, SD=0.51) produced higher scores than that of the African American females (M=3.00, SD=0). However, Hispanic male students (M=4.20, SD=0.92) yielded the higher score compared to the African American (M=4.00, SD=0), and the White (M=3.69, SD=0.48) male students. While responding to the measurement of the attitude toward the statement of "I have less anxiety in taking computer-based quizzes than paper-and-pencil quizzes," White female students (M=4.83, SD=0.39) produced higher scores than that of the African American females (M=4.00, SD=0). Yet, African American males (M=5.00, SD=0) had the higher score than that of the White (M=4.77, SD=0.6), and the Hispanic (M=4.5, SD=0.85) male peers.

About the measure of WP students' attitude toward the statement of "Computer-based math quizzes with immediate scoring helping me evaluate my own understanding and performance," the result showed that White female students (M=4.50, SD=0.52) produced higher scores than that of the African American females (M=3.67, SD=0.58). But African American males (M=4.67, SD=0.58) generally produced the higher score than that of the White males (M=4.00, SD=0.82), and of the Hispanic males (M=4.40, SD=0.84).

QUALITATIVE RESULTS

Interviews were conducted with 12 students from the WP group on the last day of the study. The interview lasted 10 minutes for each student. Students were asked to further explicate their attitudes toward mathematics, attitudes toward using computers in learning, and perception of computer-based mathematics instruction. The interview was an informal conversation, which provided students opportunities to explain their written answers as well as to orally express their feelings about web-based mathematics learning and how the web-based instruction affected their mathematics achievement. Table 8 summarizes the interviewed students' demographic data.

Interview Results

The interviewed students' attitudes toward mathematics learning. Six out of seven male students believed that they liked mathematics courses. One White and one Hispanic male student said that they liked mathematics sometimes because they thought mathematics was challenging; nevertheless, it made them think harder. Five males perceived that they could do well in mathematics, even though they were not completely sure of their ability to do math problem solving. One White male student expressed that he did not like mathematics because it was unlikely for him to get an A in the math course even when he did his very best. He did not understand why every time when he checked the answers carefully before turning in his homework or tests, he still had the wrong answers and did not receive positive results. He was regarded as a careful and diligent dil·i·gent  
adj.
Marked by persevering, painstaking effort. See Synonyms at busy.



[Middle English, from Old French, from Latin d
 student by the researcher during the time he was performing web-based tasks in the computer lab.

All of the male students believed that mathematics was useful and important for their future career. However, the majority of them did not know how mathematics learning could benefit them. One of the White male students said that mathematics would help him pursue engineering-related career. One African American male indicated that mathematics would help him to get into a college for a higher degree.

On the other hand, four out of the five female students said that they liked mathematics somewhat; and they knew that they would have to use mathematics a lot in the future; but they were unclear about the value of learning mathematics and its future application. One of the female students said that she liked mathematics because she liked to challenge herself to solve math problems. She believed that she could do well in math and was confident to solve math problems. One of the Hispanic female responded that her parents said that mathematics was good for her future; but she did not believe that she could do well in mathematics. One African American female expressed that she did not like mathematics because she usually got low scores in mathematics, and that she was not confident in doing mathematics.

The interviewed students' attitudes toward using computers in learning mathematics. This section summarized six males and five females' perceptions on advantages and disadvantages of using computer in learning. Generally, these students believed that computer supported their daily learning tasks. For example, they enjoyed typing papers, sending e-mails, playing games, listening to the music, and doing homework and practice questions on computers. Further, they believed that computers gave them opportunities to learn many new things, such as finding information about how to create animation pictures, getting information about nature, history, and movies. They could also use computers to convert units, find answers for their homework questions, checking weathers, print lyrics lyrics npl [of song] → paroles fpl

lyrics lyric npl [of song] → Text m 
 of some popular songs, and do some calculations with online calculators.

Also, they found that working with the computer made the learning process more enjoyable and stimulating. Lessons on the computer were believed to be more fun and easy to read because these lessons were more colorful, and highlighted with more tables and charts. The computer made it easier to type and erase when preparing their papers.

Nevertheless, one White male student held an attitude against computers use. He stated that "I don't don't  

1. Contraction of do not.

2. Nonstandard Contraction of does not.

n.
A statement of what should not be done: a list of the dos and don'ts.
 like computer math. I don't learn anything from the computer. Computer math gives no help and no interaction. It's hard to work with the computer." He also said that he preferred to do math with paper-and-pencil, and had somebody sit next to him telling him how to do the work. He preferred human interactions; he believed that the computer was not smart enough to provide intensive and detailed feedback on how to solve problems. He also added that his parents did not want him to spend much time on the Internet, so he did not prefer using computers in learning.

The interviewed students' perception and evaluation on computer-supported mathematics instruction. An African American male student expressed that he enjoyed computer math because computer math made him feel that he was smarter and made the problem-solving process easier. He believed that he could get high scores in math if he was given more time to practice on the computer. Another African American male said that he liked computer math because it was exciting and challenging; but he did not think that computer homework could benefit his learning because he did not have computer access at home; therefore it was impossible for him to practice math questions on the computer at home.

Two Hispanic male students said that "computer math gives more clues, gives more information and more practice." They liked doing math on the computer because it was easy to type and erase. It was easy to identify the right or wrong answers; and it was exciting to receive immediate scores. They believed that computer math made them like mathematics more; and practicing mathematics on the computer would motivate them to learn more.

Moreover, two White males believed that the computer made mathematics easier because it offered more instruction, more examples, which were more readable read·a·ble  
adj.
1. Easily read; legible: a readable typeface.

2. Pleasurable or interesting to read: a readable story.
. One of them liked the check button on the computer because it gave him an opportunity to correct his answers. Yet, he did not believe that computer math could increase his achievement scores because he could not ask questions on the computer. The other White male liked the computer scoring system Noun 1. scoring system - a system of classifying according to quality or merit or amount
rating system

classification system - a system for classifying things
 because it told him how good or bad his performance was, and it allowed him to retake re·take  
tr.v. re·took , re·tak·en , re·tak·ing, re·takes
1. To take back or again.

2. To recapture.

3. To photograph, film, or record again.

n.
1.
 the homework in order to improve his scores.

On the other hand, five female students all believed that computer math was much more interesting than paper-and-pencil math since computers made learning fun; and computer provided examples, scoring, and questions solutions to help them learn and review at the same time. One African American female particularly expressed that computer math made her understand fractions better; and she liked the short answer homework, in which she could fill numbers in the box and solve each problem step-by-step. She also thought that computers made math problems look easier and clearer. Another Hispanic female student said that this was her first time to do math on the computer, and that she really liked it. She asked if she could have the website of the computer math course, so she could have more practices at home. She preferred to practice online and receive the solutions and scores immediately after finishing her assignments.

DISCUSSION

Students' Attitude Toward Mathematics Learning and Web-Based Assessment

The analysis of multivariate analysis (MANOVA) indicates that there was no significant difference between the two groups in students' preattitude toward mathematics learning. After three weeks of receiving treatments, statistic results showed that no significant difference between group and gender existed with respect to students' postattitude toward mathematics learning. Yet, the TP group students' postattitude toward mathematics remained the same, while the overall attitudes of WP students showed some improvement.

Further, the descriptive analysis and the interview results indicated that the WP students were generally enthusiastic about their web-based learning experience. Many of WP students reported that they enjoyed working with computer assessment, and preferred to have more computer math practice. This finding was consistent with the results reported in prior studies such as the studies by O'Callaghan (1998), and by Gretes and Green (2000).

In addition, after participating in the web-based mathematics assessment and practice, Hispanic students tended to be more confident with themselves in doing math than their White peers. Those Hispanic students demonstrated a stronger positive perception in believing themselves to be able to handle more difficult math than the Whites. Further, males in the WP group generally had more positive attitudes toward statements of "I am sure of myself when I do math," "I can do well in math," "I think I could handle more difficult math," "I enjoy math problem solving," than the males in the TP group.

Nevertheless, the WP group of females showed less positive attitudes toward the statements of "I can do well in math," and "I think I could handle more difficult math," than females in the TP group after the treatment. Seventh-grade White females were found to have much stronger agreements than their African American females on the statements regarding the usefulness of web-based immediate scores on their homework, the usefulness of web-based immediate feedback for problem solving, the feature of web-based practice to mitigate mit·i·gate
v.
To moderate in force or intensity.



miti·gation n.
 anxiety, and the web-based immediate scoring for helping their understanding and performance.

Comparisons Between the Web-Based and Paper-and-Pencil Drill and Practice

Before getting into an indepth discussion of the impacts of the web-based technology on students' learning, it was essential to summarize sum·ma·rize  
intr. & tr.v. sum·ma·rized, sum·ma·riz·ing, sum·ma·riz·es
To make a summary or make a summary of.



sum
 students' experience in computer using and perception. The data shown in this study indicated that the 21st century is no longer a "penmanship" century in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. , which may not be surprising for most researchers. Even though the school participating in this study was located in the rural areas of Southern Texas, and the majority of the students were from low income families, 67% of students reported that they had computers at home, and 75% reported that they spent at least one hour on the computer per week. This finding matched with the report that "about two-thirds of all children 3 to 17 years of age lived in a household with a computer, and about one-third of all children used the Internet at home" by the National Postsecondary Education Cooperative (NPEC NPEC National Postsecondary Education Cooperative
NPEC Nonproliferation Policy Education Center
NPEC Nonprofit Enterprise Center (El Paso, TX) 
, [Phipps, 2004]). It is also true that schools with higher minority enrollments are provided more computer access than schools with lower minority enrollment (Phipps, 2004). Therefore, there should be no differences in computer using familiarity across minority and White students. The data in this study demonstrated that there was no difference in computer using attitude across all subgroups prior to the study: male and female; or African American, Hispanic, and White. It was shown that a majority of participants either agreed or strongly agreed that they enjoyed doing work on the computer and they preferred to have more lessons on the computer. Even though female and White students had the lowest minimum scores on the attitude toward computer using, the majority of students believed that it was important for them to learn how to use a computer on every learning subject.

In addition to students' computer using attitudes, it was essential to know that during the three weeks of working with web-based assessment and practice with the requirement of being familiar with the keyboard and web browser The program that serves as your front end to the Web on the Internet. In order to view a site, you type its address (URL) into the browser's Location field; for example, www.computerlanguage.com, and the home page of that site is downloaded to you. , there were no reports related to students' difficulties in computer and Internet manipulation. It was probably surprising to some researchers, but it was documented that "children and teenagers use computers and the Internet more than any other age group with 90% of children between the ages of 5 and 17 now using a computer" (Phipps, 2004). The interview notes indicated that students perceived lessons and assignments on the computer to be clearer to read, and that the mathematics problems on the computer appeared to be easier than on printed papers. Students also enjoyed the computer affordability; that is, easy to type and easy to erase. This finding was consistent with the results of comparison of computer-writing and paper-and-pencil writing in the study conducted by Russell in 1999.

Extending beyond the results from some previous studies such as studies by Russell and Haney in 1997, and by Zandvliet and Farragher in 1997, that considered the computer as merely a "glorified glo·ri·fy  
tr.v. glo·ri·fied, glo·ri·fy·ing, glo·ri·fies
1. To give glory, honor, or high praise to; exalt.

2.
 typewriter typewriter, instrument for producing by manual operation characters similar to those of printing. Corresponding to each key on the instrument's keyboard is a steel type. ," this study showed that computer-based or web-based assessment and practice had positive and extraneous effects on students' mathematical learning processes. At the end of the study, students enthusiastically expressed that they felt smarter while doing mathematics on the computer, and gained more confidence once provided with opportunities for multiple practices and receiving immediate feedback for improvement. These effects reached beyond what paper-and-pencil could do for all students.

Web-based assessment and practice provided students with immediate feedback and automated au·to·mate  
v. au·to·mat·ed, au·to·mat·ing, au·to·mates

v.tr.
1. To convert to automatic operation: automate a factory.

2.
 scores that led students to have more control over their work and their effort. The students' survey results related to their perception and evaluation of the web-based assessment indicated that the immediate feedback and instant scoring appeared to be the most attractive features of the web-based learning. These features might also affect the students' success or failure in mathematics learning. This finding reinforced the presumption A conclusion made as to the existence or nonexistence of a fact that must be drawn from other evidence that is admitted and proven to be true. A Rule of Law.

If certain facts are established, a judge or jury must assume another fact that the law recognizes as a logical
 that students highly desire confirmation of their understanding and knowing their performance. Students need to recognize their mistakes as early as possible, so that they can have the chance to correct and adjust their understanding before they start to forget how they made those mistakes. The immediate feedback, even though for some particular questions, only telling students whether their answer is correct or incorrect, is of importance to let students recognize their misunderstandings and identify the learning areas that needed to spend more time and effort for improvement.

With the immediate feedback and instant scoring, the web-based assessment and practice not only plays the role of measurement or evaluation, but it also plays the role of instruction, reflection and reinforcement (Bransford, Brown, & Cocking cock 1  
n.
1.
a. An adult male chicken; a rooster.

b. An adult male of various other birds.

2. A weathervane shaped like a rooster; a weathercock.

3. A leader or chief.
, 1999; Thorndike Thorn·dike , Edward Lee 1874-1949.

American educational psychologist noted for his study of animal intelligence and for his methods of measuring intelligence.
, 1913). Students who take web-based assessment have opportunities to show their understanding; additionally, they can learn from their responses or mistakes to clarify, review, and reconfirm re·con·firm  
tr.v. re·con·firmed, re·con·firm·ing, re·con·firms
To confirm again, especially to establish or support more firmly: reconfirmed the reservations.
 previous concepts, and finally integrate complex mathematics concepts from the multiple practicing.

Web-based assessment and practice offered students multiple practice opportunities that eventually encouraged students to spend more time on tasks and attain higher levels of achievement. The feature of the randomized item generation provided by the web-based assessment system offered students multiple versions of each homework set. Students could practice as many versions or as many times as possible when it is necessary. Along with the immediate feedback and automated scoring, the automatic item generation encouraged students (a) who highly desire a perfect performance, having an opportunity to reach the maximum scores, and (b) who are not confident with their understanding, confirming and reconfirming the mathematical concepts and procedures.

Even though some critics indicate that the benefits of drill-and-practice are only short-term memory short-term memory
n.
Abbr. STM The phase of the memory process in which stimuli that have been recognized and registered are stored briefly.
 (Carpenter & Lehrer, 1999), long-term Long-term

Three or more years. In the context of accounting, more than 1 year.


long-term

1. Of or relating to a gain or loss in the value of a security that has been held over a specific length of time. Compare short-term.
 retention can be gradually built if students are interested in their practicing, experienced with different setup See BIOS setup and install program.  items, and if they receive "score" awards for their persistence (1) In a CRT, the time a phosphor dot remains illuminated after being energized. Long-persistence phosphors reduce flicker, but generate ghost-like images that linger on screen for a fraction of a second. . Based on the results of this study, it was found that when students engaged in the web-based assessment and practice, they were willing to spend more time on tasks to gain understanding and to strive for better achievement.

Web-based assessment and practice improved students' confidence in math problem solving, reduced their anxiety in test taking, and motivated mo·ti·vate  
tr.v. mo·ti·vat·ed, mo·ti·vat·ing, mo·ti·vates
To provide with an incentive; move to action; impel.



mo
 them to learn mathematics. "Computer math makes me smarter," an African American male student said. "Computer math makes me understand fractions better," stated by an African American female student. "Computer math gives more clues, more information and more practice," a Hispanic male student indicated. "Computer math gives more fun to learn," said a White male student.

Along with the ultimate positive evaluation and perception of web-based assessment on the written survey, these statements "Computer math makes me smarter," "Computer math makes me understand fractions better," "Computer math gives more clues, more information and more practice," and "Computer math gives more fun to learn" indicated that the WP group was very enthusiastic about their learning experience. Web-based assessment not only provided students with more practice, but also helped them build better self-confidence, self-efficacy self-efficacy (selfˈ-eˑ·fi·k , and self-motivation. Additional information from the survey questionnaire and interview results also demonstrated that web-based assessment with features of immediate feedback, clear instruction, and instant scoring gave students better guidance to direct their learning.

Also, web-based mathematics assessment and practice enabled participants, who had a high level of anxiety in learning math (several of the students were math phobic pho·bic
adj.
Of, relating to, arising from, or having a phobia.

n.
One who has a phobia.
), to recognize their scores instantly; thus, they might have more control over their learning, and felt less anxious about doing math. It was apparent that the web-based multiple practices fostered students' self-assessment and self-regulation in which students could assess what they already know and what they need to improve, to make their knowledge base compatible with the learning goals. From this point of view, web-based assessment truly scaffolded students' learning processes (Bransford et al., 1999).

IMPLICATIONS

More research on the influence of web-based assessment and practice on students' performance should be conducted in different schools and at different grade levels to confirm the actual benefits of the online delivery system. In the future research, web-based assessment systems should be implemented for classroom assignments and practices, and should be assigned to students by their own teachers in addition to the traditional assessment over an entire school year. The measurement of the mathematics achievement and attitude should be the results of the long-term study across a diverse population (i.e., the future research should modify this present study by including more students from different ethnicity, such as Asian and Native American).

Technically, more web-based assessment tasks on various mathematical concepts and strands should be designed. The database system should be constructed to manipulate manipulate

To cause a security to sell at an artificial price. Although investment bankers are permitted to manipulate temporarily the stock they underwrite, most other forms of manipulation are illegal.
 a large-scale data collection, and to generate item pools for different mathematical levels. An implementation of diagnostic systems for different mathematical strands is also suggested to enrich the automatic feedback to teachers and educators.

References

Aiken, L. R., & Dreger, R. M. (1961). The effects of attitudes on performance in mathematics. Journal of Educational Psychology, 52(1), 19-24.

Allen, G. D. (2001). Online calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. : The course and survey results. Computers in the Schools: The Interdisciplinary in·ter·dis·ci·pli·nar·y  
adj.
Of, relating to, or involving two or more academic disciplines that are usually considered distinct.


interdisciplinary
Adjective
 Journal of Practice, Theory, and Applied Research, 17(1/2), 17-30.

Allen, R. (1998). The web: Interactive and multimedia education. Computer Networks and ISDN ISDN
 in full Integrated Services Digital Network

Digital telecommunications network that operates over standard copper telephone wires or other media.
 Systems, 30(16-18), 1717-1727.

Anderson, J. R. (1995). Cognitive psychology cognitive psychology, school of psychology that examines internal mental processes such as problem solving, memory, and language. It had its foundations in the Gestalt psychology of Max Wertheimer, Wolfgang Köhler, and Kurt Koffka, and in the work of Jean  and its implications, (4th ed), New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: W.H. Freeman Freeman can mean:
  • An individual not tied to land under the Medieval feudal system, unlike a villein or serf
  • A person who has been awarded Freedom of the City or "Freedom of the Company" in a Livery Company
  • The Freeman
 and Company.

Bennett, R. E. (2001). How the Internet will help large-scale assessment reinvent re·in·vent  
tr.v. re·in·vent·ed, re·in·vent·ing, re·in·vents
1. To make over completely: "She reinvented Indian cooking to fit a Western kitchen and a Western larder" 
 itself. Education Policy Analysis Archives Education Policy Analysis Archives is a peer-reviewed, open access scholarly journal created in 1993 by Gene V. Glass at Arizona State University. Articles are published in English, Spanish or Portuguese. , 9(5). Retrieved on February 19, 2006, from http://epaa.asu.edu/epaa/v9n5.html

Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn. Washington, DC: National Academy Press.

Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19-32). Mahwah, NJ: Lawrence Erlbaum.

Chi, M. T. H., Lewis, M. W., Reiman, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science cognitive science

Interdisciplinary study that attempts to explain the cognitive processes of humans and some higher animals in terms of the manipulation of symbols using computational rules.
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DIEM M. NGUYEN

Bowling Green State University Bowling Green State University, at Bowling Green, Ohio; coeducational; chartered 1910 as a normal school, opened 1914. It became a college in 1929, a university in 1935.  

USA

dnguyen@bgsu.edu

YI-CHUAN JANE HSIEH

Ching Yun University History
The Presidents
Organization
A president (校長) heads the University. Each college (院) is headed by a dean (院長), and each department (系) by a chairman (系主任).
 

Taiwan

ychsieh@cyu.edu.tw

G. DONALD ALLEN Donald Merriam Allen (b. Iowa, 1912 — d. San Francisco, August 29, 2004), influential editor, publisher, and translator of contemporary American literature. He is perhaps best known for his project The New American Poetry 1945-1960  

Texas A & M University

USA

dallen@math.tamu.edu
Table 1 Component (Factor) Transformation Matrix

           1 (the value of                              3 (the value of
           computer usage in  2 (positive affection of  studying
component  learning)          doing mathematics)        mathematics)

1           .812               .472                     .343
2          -.531               .841                     .100
3          -.241              -.263                     .934

Table 2 Rotated Component Matrix

Variables                          Component 1  Component 2  Component 3

I enjoy doing things on a          .760
  computer
I concentrate on a computer when   .611
I use one.
I would work harder if I could     .695
  use computers more often.
I know that computers give me      .584
  opportunities to learn many new
  things.
I enjoy lessons on the computer.   .511
I believe that the more teachers   .786
  use computers, the more I will
  enjoy school.
I feel comfortable working with a  .830
  computer.
I think that working with a        .850
  computer is enjoyable and
  stimulating.
I have a lot of self-confidence    .752
  when it comes to working with
  computers.
I enjoy mathematics courses.                    .779
I feel at ease in mathematics.                  .790
I am sure of myself when I do                   .717
  math.
I know I can do well in math.                   .739
I think I could handle more                     .864
  difficult math.
I enjoy mathematics problem                     .664
  solving.
I will need mathematics for my                               .854
  future work.
I study math because I know how                              .721
  useful it is.
Knowing mathematics will help me                             .779
  earn a living.

Table 3 Component (Factor) Transformation Matrix

                                                       3 (the value of
           1 (the general          2 (positive         computer-based
           perception of learning  affection of doing  mathematic
component  math on computers)      mathematics)        instruction)

1           .801                   .352                 .485
2          -.415                   .910                 .025
3           .432                   .221                -.874

Table 4 Rotated Component Matrix

Variables                          Component 1  Component 2  Component 3

I like to do math on the           .872
  computer.
Computer-based math tasks are      .716
  clear and easy to read.
I like to receive immediate        .875
  scores on my math homework and
  quizzes from the computer.
Immediate scores help me to be     .743
  aware of my performance.
Computer immediate feedback helps  .575
  me to recognize my mistakes
  instantly.
Computer-based math homework       .599
  gives me more chance to
  practice.
Computer-based quizzes help me to  .800
  be less anxious in waiting for
  my scores.
I have less anxiety in taking      .633
  computer-based quizzes than
  paper-and-pencil quizzes.
Computer-based math quizzes with   .677
  immediate scoring help me
  evaluate my own understanding
  and performance.
I like computer-based math         .891
  quizzes more than paper-and-
  pencil quizzes.
I enjoy mathematics course.                     .781
I am sure of myself when I do                   .791
  math.
I know I can do well in math.                   .806
I think I would handle more                     .828
  difficult math.
I enjoy mathematics problem                     .836
  solving.
I study math because I know how                 .725
  useful it is.
I like the help and suggestions                              .539
  on my math homework from the
  computer.
Computer immediate feedback is                               .746
  useful for mathematics problem
  solving.
Computer-based mathematics                                   .797
  instruction helps me to review
  mathematics concepts.

Table 5 Multivariate Tests

Effect                             Value  F      Hypothesis df

GENDER          Pillai's Trace      .523   .930  20.000
                Wilks' Lambda       .477   .930  20.000
                Hotelling's Trace  1.094   .930  20.000
ETHNIC          Pillai's Trace     1.058  1.010  40.000
                Wilks' Lambda       .213   .991  40.000
                Hotelling's Trace  2.419   .968  40.000
GENDER *ETHNIC  Pillai's Trace      .763  2.741  20.000
                Wilks' Lambda       .237  2.741  20.000
                Hotelling's Trace  3.224  2.741  20.000

Effect                             Error df  Sig.   Eta squared

GENDER          Pillai's Trace     17.000    .566   .523
                Wilks' Lambda      17.000    .566   .523
                Hotelling's Trace  17.000    .566   .523
ETHNIC          Pillai's Trace     36.000    .490   .529
                Wilks' Lambda      34.000    .515   .538
                Hotelling's Trace  32.000    .544   .547
GENDER *ETHNIC  Pillai's Trace     17.000    .020*  .763
                Wilks' Lambda      17.000    .020*  .763
                Hotelling's Trace  17.000    .020*  .763

* p < .05

Table 6 Tests of Between-Subjects Effects

         Dependent                            Type III sum       Mean
Source   variables                            of squares    df   squared

ETHNIC   ...                                  ...           ...  ...
         I am sure of myself when I do math.  9.222         2    4.611
GENDER*  ...                                  ...           ...  ...
ETHNIC   I enjoy mathematics course.           .919         1     .919
         I am sure of myself when I do math.  3.257         1    3.257
         I know I can do well in math.         .110         1     .110
         I think I would handle more           .827         1     .827
         difficult math.
         I enjoy mathematics problem           .191         1     .191
         solving.
         I study math because I know how       .179         1     .179
         useful it is.
         I like to do math on the computer.    .368         1     .368
         Computer-based math tasks are clear  1.088         1    1.088
         and easy to read.
         I like to receive immediate scores   1.813         1    1.813
         on my math homework and quizzes
         from the computer
         Immediate scores help me to be        .879         1     .879
         aware of my performance.
         I like the help and suggestions on   6.440E-       1    6.440E-
         my math homework from the computer.    02                 02
         Computer immediate feedback helps     .704         1     .704
         me to recognize my mistakes
         instantly.
         Computer immediate feedback is       3.596         1    3.596
         useful for mathematics problem
         solving.
         Computer-based math homework gives    .776         1     .776
         me more chance to practice.
         Computer-based mathematics           7.558E-       1    7.558E-
         instruction helps me to review         02                 02
         mathematics concepts.
         Computer-based quizzes help me to     .280         1     .280
         be less anxious in waiting for my
         scores.
         I have less anxiety in taking        1.369         1    1.369
         computer-based quizzes than
         paper-and-pencil quizzes.
         Computer-based math quizzes with     2.721         1    2.721
         immediate scoring help me evaluate
         my own understanding and
         performance.
         I like computer-based math quizzes    .272         1     .272
         more than paper-and-pencil quizzes.
Error    ...                                  ...           ...  ...

         Dependent                                          Eta
Source   variables                            F      Sig.   squared

ETHNIC   ...                                  ...    ...    ...
         I am sure of myself when I do math.  4.253  .022*  0.191
GENDER*  ...                                  ...    ...    ...
ETHNIC   I enjoy mathematics course.           .973  .330    .026
         I am sure of myself when I do math.  3.003  .092    .077
         I know I can do well in math.         .114  .738    .003
         I think I would handle more           .537  .468    .015
         difficult math.
         I enjoy mathematics problem           .117  .735    .003
         solving.
         I study math because I know how       .161  .691    .004
         useful it is.
         I like to do math on the computer.    .832  .368    .023
         Computer-based math tasks are clear  2.331  .136    .061
         and easy to read.
         I like to receive immediate scores   4.134  .049*   .103
         on my math homework and quizzes
         from the computer
         Immediate scores help me to be       1.942  .172    .051
         aware of my performance.
         I like the help and suggestions on    .116  .735    .003
         my math homework from the computer.
         Computer immediate feedback helps    1.394  .246    .037
         me to recognize my mistakes
         instantly.
         Computer immediate feedback is       8.468  .006*   .190
         useful for mathematics problem
         solving.
         Computer-based math homework gives   2.056  .160    .054
         me more chance to practice.
         Computer-based mathematics            .146  .705    .004
         instruction helps me to review
         mathematics concepts.
         Computer-based quizzes help me to    1.007  .322    .027
         be less anxious in waiting for my
         scores.
         I have less anxiety in taking        3.952  .054*   .099
         computer-based quizzes than
         paper-and-pencil quizzes.
         Computer-based math quizzes with     5.229  .028*   .127
         immediate scoring help me evaluate
         my own understanding and
         performance.
         I like computer-based math quizzes    .852  .362    .023
         more than paper-and-pencil quizzes.
Error    ...

* p < .05

Table 8 Demographic Description of the Interviewed Students

        African American  Hispanic  White

Male    2                 2         3
Female  1                 2         2
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