The effectiveness of long term vs. short term training in selected computing technologies on middle and high school mathematics teachers' attitudes and beliefs.This article describes two professional development experiences for middle and high school mathematics teachers: one 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. , the other short-term Short-term Any investments with a maturity of one year or less. short-term 1. Of or relating to a gain or loss on the value of an asset that has been held less than a specified period of time. . The training of the long-term group (n=12) took place over an entire semester se·mes·ter n. One of two divisions of 15 to 18 weeks each of an academic year. [German, from Latin (cursus) s , in a 15-week, 45-hour graduate course, at an urban institution in New York City New York City: see New York, city. New York City City (pop., 2000: 8,008,278), southeastern New York, at the mouth of the Hudson River. The largest city in the U.S. , that accented the use of computing computing - computer technologies, especially the "TI83 Plus" graphing calculator Graphing Calculator may refer to:
********** Microcomputers and calculators are entering classrooms in substantial numbers, with attractive software applications, advanced multimedia capabilities and, above all, the World Wide Web. Research interest in the use of calculators and computing technologies in education has increased dramatically over the past decade because of this technology-enriched environment. In such settings, technology impacts not only what is taught and how it is taught but also what students learn and how they learn it (Beckmann Beck·mann , Max 1884-1950. German artist whose early expressionistic manner yielded to his lasting style, the painting of brutal, often grotesque figurative canvases, such as Night (1919). , Thompson Thompson, city, Canada Thompson, city (1991 pop. 14,977), central Man., Canada, on the Burntwood River. A mining town, it developed after large nickel deposits were discovered in the area in 1956. , & Senk, 1999). This has posed a challenge and an opportunity for teachers to learn more about computers and software, and how to integrate technology to teach or to enhance their curricula. Research has shown, however, that providing support for the use of technology in the schools is only half the issue; the other half involves changing attitudes and mental structures (Thatcher Thatch·er , Margaret Hilda. Baroness. Born 1925. British Conservative politician who served as prime minister (1979-1990). Her administration was marked by anti-inflationary measures, a brief war in the Falkland Islands (1982), and the passage of a , 1996). Positive teacher attitudes toward technology are necessary for its effective use in the classroom (Lawton Lawton, city (1990 pop. 80,561), seat of Comanche co., SW Okla.; inc. 1901. It is a commercial and trade center for the surrounding cotton, wheat, and cattle area. Fort Sill is the largest local civilian employer. & Gerschner, 1982; Woodrow Woodrow may refer to:
v. suf·ficed, suf·fic·ing, suf·fic·es v.intr. 1. To meet present needs or requirements; be sufficient: These rations will suffice until next week. to train teachers? This article presents findings from a study that involved two groups of mathematics teachers who were trained to use selected computing technologies through two different professional development experiences: one long-term, the other short-term. The training of the long-term group took place over an entire semester, in a 15-week, 45-hour graduate course. The training of the short-term group took place in a series of three workshops totaling 7 hours. Changes in teacher attitudes and beliefs due to the technology training are presented. Role of Technology in Mathematics Instruction Computing-technologies have the potential for wide-ranging wide-rang·ing adj. Covering a wide area; including much: a pianist's wide-ranging repertoire; a wide-ranging interview. and long-lasting adj. 1. Existing or persisting for a long time; as, a long-lasting friendship s>. Adj. 1. long-lasting - existing for a long time; "hopes for a durable peace"; "a long-lasting friendship" impact in the mathematics classroom (Heid & Baylor Bay·lor , Elgin Born 1934. American basketball player. He was a forward for the Minneapolis and Los Angeles Lakers from 1958 to 1971 and ranks among the all-time National Basketball Association leaders in points and per-game scoring average. , 1993). They facilitate in-depth in-depth adj. Detailed; thorough: an in-depth study. in-depth Adjective detailed or thorough: an in-depth analysis exploration of mathematical topics previously too complex for typical classrooms, especially when such topics involve real-world, "messy mess·y adj. mess·i·er, mess·i·est 1. Disorderly and dirty: a messy bedroom. 2. Exhibiting or demonstrating carelessness: messy reasoning. " data. They also give all students, whether functioning at Piaget's concrete or formal operational level, the technology tools that enable them to visually examine "concrete" representations of mathematics concepts (Shoaf-Grubbs, 1992; Hollylynne, Dawson Dawson or Dawson City, city (1991 pop. 972), W Yukon Territory, Canada, at the confluence of the Yukon and Klondike rivers. It is the trade center of the Klondike mining region and a tourist center. , & Garofalo Garofalo as a surname may refer to:
tr.v. for·mal·ized, for·mal·iz·ing, for·mal·iz·es 1. To give a definite form or shape to. 2. a. To make formal. b. level of understanding" (Shoaf-Grubbs, 1992, p.30). The 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 ) has argued even more persuasively per·sua·sive adj. Tending or having the power to persuade: a persuasive argument. per·sua in support of the use of computing technologies in the classroom.
Electronic technologies-calculators and computers- are essential
tools for teaching, learning, and doing mathematics. They furnish
visual images of mathematical ideas, they facilitate organizing and
analyzing data, and they compute efficiently and accurately. They
can support investigation by students in every area of mathematics,
including geometry, statistics, algebra, measurement, and number.
When technological tools are available, students can focus on
decision-making, reflection, reasoning and problem solving (NCTM,
2000, p.24).
Mathematics Teachers' Attitudes and Beliefs Toward Technology Even though NCTM's conclusions value the use of technology in the mathematics classroom, research on mathematics teachers' beliefs and attitudes toward such use indicates that firmly held tenets are resistant to change. Teachers have continued not to want to face the uncertainties related to the use of computing technologies in the classroom, and often question whether students will do as well with technology as with traditional methods. In 1988, Dick and Shaughnessy This article is about the neighborhood in Vancouver, B.C.; for other uses, see Shaughnessy (disambiguation). Shaughnessy is an almost entirely residential neighbourhood in Vancouver, British Columbia, Canada, spanning about 447 hectares[1] studied the effects of providing classroom sets of symbolic-manipulation calculators for volunteer high school mathematics teachers. Despite the change in attitudes for both their male and female students, "teachers felt that the use of the calculators brought only minor changes in the dynamic of classroom interaction" (p.333). Tharp Tharp , Twyla Born 1941. American dancer and choreographer whose works, such as Deuce Coupe (1973), combine jazz, tap, ballet, and modern dance. Noun 1. , James James, person in the Bible James, in the Gospel of St. Luke, kinsman of St. Jude. The original does not specify the relationship. James, rivers, United States James. , Fitzsimmons, and Ayers "Ayers" may refer to:
See also: favor viewing the graphing calculator as a "thinking tool" to enhance conceptual understanding. However, data from questionnaires administered revealed a significant correlation between holding a more rule-based viewpoint about learning mathematics and the view that graphing calculators do not enhance instruction and may even hinder hin·der 1 v. hin·dered, hin·der·ing, hin·ders v.tr. 1. To be or get in the way of. 2. To obstruct or delay the progress of. v.intr. it. Tharp et al. concluded that rule-based teachers are most likely to quickly return to lecture mode after engaging in initial instructional experiences with graphing calculators. Models of Professional Development Short-term forms of professional development, most often in the guise Guise (gēz, gwēz), influential ducal family of France. The First Duke of Guise The family was founded as a cadet branch of the ruling house of Lorraine by Claude de Lorraine, 1st duc de Guise, 1496–1550, who received of one or two-shot workshops, continue to be most commonly used 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. to support teachers in implementing innovative programs in to classroom. As such, school districts are able to avoid the expenses--in personnel and resources--entailed in long term professional development that might extend to a full academic semester or full-year commitment. Such forms of training have no continuity, and no follow-up follow-up, n the process of monitoring the progress of a patient after a period of active treatment. follow-up subsequent. follow-up plan , and leave teachers with the decision to continue on their own (Zigarmi, Betz Betz may refer to:
Johannes Vilhelm Jensen , 1977; Clarke Clarke , Arthur Charles Born 1917. British writer, scientist, and underwater explorer noted for his stories of space exploration. His works include 2001: A Space Odyssey (1968). , 1994). The danger is that teachers are usually not 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 to implement any new program if they are not convinced of its effectiveness, therefore annihilating an·ni·hi·late v. an·ni·hi·lat·ed, an·ni·hi·lat·ing, an·ni·hi·lates v.tr. 1. a. To destroy completely: The naval force was annihilated during the attack. any potential for change and improvement. Today, such form of training has not changed much across the US. A recent CEO (1) (Chief Executive Officer) The highest individual in command of an organization. Typically the president of the company, the CEO reports to the Chairman of the Board. forum (1999) reports that districts spend only about 1% of their technology budget on teacher training, far less than the U.S. Department of Education recommended amount of 30%. If the goal for schools and educators is to improve student achievement, this situation needs to change. The role of technology in education and in society will only increase, and research has shown that not only does effective technology training of teachers change their attitudes, but also it positively affects student achievement (Christensen, 2002). It is clear from a review of the research that a model of professional development that provides teachers with time to design a plan for using suggested materials and methods in their classrooms resulting in greater educational gains for students, will be the catalyst to initiate a shift in teachers' attitudes. For instance, a study within the Apple Classrooms of Tomorrow (ACOT ACOT Apple Classrooms of Tomorrow ACOT A Cherry on Top ACOT American College of Technology (Saint Joseph, MO) ACOT Atlantic Coast Old Timers ACoT Associateship of the College of Teachers (UK) ), a multi-year project that provides support for technology integration in the classroom, showed that significant changes in attitudes among participant teachers happened only during the second year of the project. Teachers felt comfortable using technology in their classrooms only after personal appropriation The designation by the government or an individual of the use to which a fund of money is to be applied. The selection and setting apart of privately owned land by the government for public use, such as a military reservation or public building. of the technology tools had taken place (Dwyer Dwyer may refer to: People with the Surname Dwyer
n. pl. pro·fi·cien·cies The state or quality of being proficient; competence. Noun 1. proficiency - the quality of having great facility and competence and providing time for sharing ideas are key elements in the training of teachers that would foster significant and lasting change on their attitude toward the use of technology in the classroom. Porter, Garet, Desimone, Yoon, and Birman Birman a longhaired breed of cat with blue eyes and a light body with darker points (ears, face, legs and tail) in colors similar to the Siamese. The paws are white ('gloves'). Called also Sacred Cat of Burma. The breed is affected by an inherited polyneuropathy. (2000), found in their longitudinal lon·gi·tu·di·nal adj. Running in the direction of the long axis of the body or any of its parts. large-scale study that examined the effectiveness of professional development on improving classroom teaching practice for mathematics and science teachers that a high quality professional development depends in large measure on six features: form, duration, collective participation, content, active learning, and coherence coherence, constant phase difference in two or more Waves over time. Two waves are said to be in phase if their crests and troughs meet at the same place at the same time, and the waves are out of phase if the crests of one meet the troughs of another. . Activities of longer duration (long-term training) and activities that encourage collective participation of teachers tend to place more emphasis on content than other activities, provide more opportunities for active learning, provide a more coherent professional development, and lead to teachers reporting enhanced knowledge and skill and change in teaching practices (Porter et al., 2000). This article describes the results of a study of two groups of mathematics teachers who were trained to use graphing calculators and specialized spe·cial·ize v. spe·cial·ized, spe·cial·iz·ing, spe·cial·iz·es v.intr. 1. To pursue a special activity, occupation, or field of study. 2. software in two different professional development models. The first group included middle and high school mathematics teachers enrolled in a 15-week, 45-hour graduate course needed to complete requirements for their advanced degree in mathematics education. The second group was comprised of middle school mathematics teachers from the college's Professional Development School (PDS (1) (Processor Direct Slot) A single expansion slot on certain, early Macintosh models that was used to connect high-speed peripherals as well as additional CPUs. Providing a channel directly to the CPU, the PDS coexisted with NuBus slots on some models. ). They received a short-term training of a series of three workshops. The researcher sought to determine whether teachers' beliefs and attitudes about the use of technology in the mathematics classroom changed as a result of long-term vs. short-term professional development. METHOD Context The course and its participants. Participants in the Spring 2001 semester graduate course (n = 12) included four female and eight male teachers, eleven of whom were matriculated students in the Master's of Mathematics Education program. Of the 12 teachers, six taught in middle school, and six taught in high school. They used the TI83-Plus (Texas Instrument, 2001) for most of each of 10 sessions, and the Geometer's Sketchpad (Key Curriculum Press, 2001) for most of each of 3 sessions. Not a single teacher had ever used the TI83 Plus graphing calculator in teaching mathematics concepts, nor had known about the Geometer's Sketchpad prior to taking the course. The investigator chose this course for the study because it was redesigned to meet the request of students in the Master's program. They had indicated through the annual evaluation survey given by the Division of Education of the college that they would like to see more technology integrated in mathematics education courses. Responding to teachers' requests in a manner consistent with their expectations is a key element of a successful professional development experience (Clarke, 1994). In redesigning the course however, the path recommended by Stein Stein , William Howard 1911-1980. American biochemist. He shared a 1972 Nobel Prize for pioneering studies of ribonuclease. , Smith, and Silver (1999) was followed. That is, the teaching of teachers for the 21st century should be done in a new way. The topics in this course offered the opportunity to introduce these teachers to technology in mathematics teaching that support and facilitate conceptual development of mathematics content in the context of the curriculum they are teaching. Teacher's participation to the study was voluntary. They were informed that lack of participation would have no influence on the course grade. All teachers' names in this article are pseudonyms This article gives a list of pseudonyms, in various categories. Pseudonyms are similar to, but distinct from, secret identities. Artists, sculptors, architects
The workshops and its participants. This group of participants (n=11), which included six female and five male teachers, attended three workshops during the 2001 Fall Semester. They were first exposed to an algebra algebra, branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Algebra is a generalization of arithmetic and gains much of its power from dealing symbolically with elements and operations (such as computer-based manipulative ma·nip·u·la·tive adj. Serving, tending, or having the power to manipulate. n. Any of various objects designed to be moved or arranged by hand as a means of developing motor skills or understanding abstractions, especially in called Virtual Tiles (Bradford, 1996) in one three-hour session, then introduced to Geometer's Sketchpad activities in one two-hour session, before they studied and discovered some key concepts in pre-algebra, algebra, and statistical analysis with the TI83-Plus graphing calculator, also in one two-hour session. Prior to these workshops, none of these teachers had used some kinds of technology to teach mathematics concepts. The researcher spends each semester one day a week at the PDS as the college's liaison to the site, supervising student teachers, and working with practicing teachers towards yearly PDS goals identified by the two partners as in a model suggested by Teitel (2001). The technology training of PDS teachers took place because one of the year's main PDS goals was to increase mathematics teachers' awareness of technology-based curricula. The two partners made the decision to use the only two citywide Professional Development Days available that year, to conduct three workshops to train them on how to use computing technologies to enhance the curriculum. Time constraints In law, time constraints are placed on certain actions and filings in the interest of speedy justice, and additionally to prevent the evasion of the ends of justice by waiting until a matter is moot. and lack of materials were the barriers that made it impossible for the researcher to work with teachers at any other time during the year. At the time of the training, not much computing technologies was available at the PDS site, other than scattered Scattered Used for listed equity securities. Unconcentrated buy or sell interest. sets of four computers in each classroom. Teachers had no uses for those computers. They often question their ability to use them with 30 students or more in a classroom. The two partners however, have developed plans to create computer labs, and have designed a course that would be co-taught at the site by faculty from both institutions who would train mathematics and science teachers on developing curriculum materials that use technology. Procedures To determine the changes in teachers' beliefs and attitudes about the use of technology in the mathematics classroom, the same survey (see Appendix A) was given to both groups of teachers at the beginning and at the end of the training. Additionally, course participants submitted reflections about the training, and gave their insights regarding the role of technology in the mathematics classroom at the end of the course. Insights from workshop participants were obtained through the evaluation form given at the end of the second professional development day. Instrument The researcher did a quantitative analysis Quantitative Analysis A security analysis that uses financial information derived from company annual reports and income statements to evaluate an investment decision. Notes: of the data that was based on the pre- pre- word element [L.], before (in time or space). pre- pref. 1. Earlier; before; prior to: prenatal. 2. and post-survey results of all teacher participants. The survey, designed by Tharp et al. (1997), included 16 background questions as well as Likert-scale statements (with responses ranging from 0 = Strongly Disagree to 4 = Strongly Agree) dealing with teaching mathematics and using calculators in the classroom such as: (a) teacher view of calculator use, (b) teacher view of mathematics learning, (c) access to calculators, (d) teacher efficacy, (e) student efficacy, and (f) administrative support. The attitude-based survey was used to measure a perspective on mathematics learning: "the view of learning math as Mathematics courses named Math A, Maths A, and similar are found in:
n. 1. Orient The countries of Asia, especially of eastern Asia. 2. a. The luster characteristic of a pearl of high quality. b. A pearl having exceptional luster. 3. toward processes which involves the manipulation of symbols and 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: of facts as opposed to the view that mathematics learning is based on reasoning about relationships and patterns (Tharp et al., 1997). The measure is fairly new and has therefore no reliability and validity information available. However, this measure has concurrent validity concurrent validity, n the degree to which results from one test agree with results from other, different tests. with a Perry Measure of r = -0.43 with p < 0.05 (Tharp & Lovell, 1995). In this study however, the questionnaire was mainly intended to determine whether attitudes and beliefs about technology could change between the beginning and the end of a training program that integrates the use of technology in the mathematics classroom. Consequently, only the responses to the six statements 1, 2, 3, 4, 14, and 15, could be considered to determine if a view was favorable fa·vor·a·ble adj. 1. Advantageous; helpful: favorable winds. 2. Encouraging; propitious: a favorable diagnosis. 3. or not favorable to the use of graphing calculators. For instance, for questions 1, 4, 14, and 15, if one disagreed or strongly disagreed, his/her position was considered favorable to the use of graphing calculators or technology. For questions 2 and 3, if one agreed or strongly agreed, his/her position was also deemed favorable. Otherwise, the position was classified undecided--a response of 2--or unfavorable. The methods employed were also interpretive in·ter·pre·tive also in·ter·pre·ta·tive adj. Relating to or marked by interpretation; explanatory. in·ter pre·tive·ly adv. , in that they involved
an analysis of teachers' comments and reflections about the use of
the graphing calculators and computing technologies in the mathematics
classroom. Course participants submitted reflections about the ways the
course has contributed to their belief--or disbelief--about the
effectiveness of computing technologies. Workshop participants gave
their insights through an evaluation form given at the end of the last
professional development day.
Data Treatment To analyze the differences between the two groups, a 2X2 analysis 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 with repeated measures was performed. The first factor was Group (Course vs. PDS), and the second factor, the repeated measure, was Test (Pre-survey, Post-survey). For each item of the survey, such measure allowed the researcher to determine if the interactions between the two groups were significant, and if the differences between the pre- and post- post- word element [L.], after; behind. post- pref. 1. After; later: postpartum. 2. Behind; posterior to: postaxial. survey responses of all participants were also significant. Additionally, within each group, each question item 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 a paired-sample t-test t-test, n an inferential statistic used to test for differences between two means (groups) only. This statistic is used for small samples (e.g., N < 30). Also called t-ratio, stu-dent's t. showing the mean difference between the pre and post-survey responses. RESULTS Table 1 shows a pre-survey average response of 2.25 for the course, which appears to indicate that the course participants were undecided since a rank of 2 is midway Midway, island group (2 sq mi/5.2 sq km), central Pacific, c.1,150 mi (1,850 km) NW of Honolulu, comprising Sand and Eastern islands with the surrounding atoll. Discovered by Americans in 1859, Midway was annexed in 1867. A cable station was opened in 1903. between the most favorable (0) and the least favorable answer (4). For the post-survey, the mean average of .67 shows that course participants' attitudes changed significantly (p<.05) as they disagreed with the statement "Calculators should 'only' be used to check work." The PDS (Workshop) group results showed no significant differences between the pre- and post-survey average responses of 1.45 and 1.36. It appears however, that these participants did have a favorable attitude toward the use of calculator before and after the training, since both pre- and post-survey scores were close to the second most favorable response, 1, which was also the most selected response (the mode) by 8 teachers. The results also show that when combined, all participants (N=23) significantly (p<.05) changed their attitudes on Item 1. Table 2 shows that, on Item 2, no significant changes between pre-and post-survey responses were recorded for the course, workshop participants, and altogether. The pre- and post-survey mean responses were all close to 2, which may lead to believe that all teachers were somewhat "undecided" since a rank of 2 is midway between the most favorable (4) and the least favorable answer (0). However, the post-survey responses which were most selected by 16 of 23 teachers responding to this item was 3 or 4. Demonstrating that, perhaps, there was a small shift in favor of the statement "A graphing calculator can be used as a tool to solve problems I could not solve before," despite the non-significant mean difference of -.30 (p>.1). An analysis of Table 3 and Table 4 shows that course and workshop participants had a favorable view about the use of graphing calculators on Item 3 and Item 4. Most teachers agreed with the statement (3) "Using a graphing calculator to teach mathematics or science allows me to emphasize the experimental nature of the subject," and disagreed with (4) "Using a graphing calculator to teach math or science does not enhance student learning or understanding of concepts" before and after the training. The pre- and post-survey mean responses recorded on these two items show a favorable belief that graphing calculator can enhance student learning. For Item 14 shown in Table 5, there was a significant change of attitude for course participants. The pre-survey mean response of 2.58, shows that prior to the course, participants were favorable (agreed with) to the statement "Students lack the ability to work with a calculator as complex as graphing calculator." Six (6) of 12 teachers chose the response 3 (agree) or 4 (strongly agree). However, the post-survey mean response of 1.25 was a clear indication that a shift has taken place, since most teachers (7) choose a response of a rank of 1 (agree) or 0 (strongly disagree). The mean difference of 1.50 was significant (p<.05). The attitudes for all participants also changed significantly (P < .05). In contrast, pre- and post-survey average responses of 2.27 and 2.36 show that PDS teachers were undecided prior to and after the workshops. Finally, Table 6 shows that both groups seem to have shifted from an undecided position to a "somewhat" favorable position Noun 1. favorable position - the quality of being at a competitive advantage favourable position, superiority advantage, vantage - the quality of having a superior or more favorable position; "the experience gave him the advantage over me" with Item 15, "If students are taught to use technology, they will come to rely on it and lose their ability to think." The course recorded pre- and post-survey average responses of 1.92, and 1.25, whereas the workshop recorded pre- and post-survey average responses of 1.73 and 1.45. Even though in both groups the mean differences were not significant (p > .05), the post-survey average responses were close to 1, the second most favorable position. The overall change for the two groups combined was also not significant. DISCUSSION For the course participants, a favorable shift significantly took place on only two items, 1 "Calculators should 'only' be used to check work," and 14 "Students lack the ability to work with a calculator as complex as graphing calculator." On each of the other four items (2, 3, 4, and 15), however, the post-survey average response (2.75, 3.17, .50, and 1.25) was closer to the response that was considered to be the second most favorable to the use of graphing calculators in the classroom, demonstrating that teachers did improve attitude in favor of the use of technology in the mathematics classroom. Moreover, the significant difference on Item 14 seems to indicate that teachers' view and perception about students' ability to work with the graphing calculator grew more favorably fa·vor·a·ble adj. 1. Advantageous; helpful: favorable winds. 2. Encouraging; propitious: a favorable diagnosis. 3. as did their own ability and confidence to use this particular technology tool. What may explain the course's positive outcomes may be the length and extent to which concepts were studied. It took teachers 15 consecutive weeks to learn, practice, reflect, and be tested on the different activities involving the "TI83 Plus" graphing calculator and the Geometer's Sketchpad. During these class sessions, teachers were exposed in depth to a variety of mathematics topics with the opportunity to design one or more activities involving the use of these technology tools. They not only discussed issues that were related to the use of technology in the mathematics classroom, but also submitted reflections as answers to specific questions about their pre- and post-training beliefs and attitudes. At the end, most wrote that their pre-training beliefs and attitudes were the consequence of their lack of opportunity to experience the use of technology in a way similar to what they did in the course, and of their lack of confidence in their ability to design activities to enhance the mathematics curriculum. In general, a shift in their attitudes was however apparent, way before the end of the course, as teachers got exposed to how different concepts can be introduced through simple discovery using technology, whether with the graphing calculator or with the Geometer's Sketchpad. Many teachers decided to experiment teaching mathematics concepts using the TI-83 graphing calculators in their classes, and reported on students' reactions and on the success of the experiments (Such reports will be the subject of a second study involving middle and high school students). For the workshop group, the training seemed to have had no effects on its participants' views about the use of technology in the mathematics classroom. The differences between the pre- and post-survey mean responses were very small and were not significant on any of the six items. Such results were not surprising since the length and the extent to which the concepts presented to PDS teachers were very short, and their experiences with technology limited because of time constraints. They attended only one three-hour session and two two-hour sessions more than a month later. They were not tested, nor were they asked to design and implement technology-oriented activities. There was no continuity or follow-ups in the concepts studied. They just had a glimpse of some of the possibilities that could be used and may not have had enough time and training for a better appreciation of the effectiveness of the technology tools presented to them. What was unexpected however, was PDS teachers' initial view about the use of technology in the classroom. Pre-survey average responses show that they had a "somewhat favorable" position on five out of the six items prior to beginning the workshops, perhaps explaining the no-effects of the workshops. It is also possible that PDS teachers had had previous technology training that was positive and/or had experienced positive outcomes for themselves or their students. CONCLUSIONS An analysis of course participants' comments and reflections show that all agreed on the nature of technology as a great motivational tool as demonstrated by what one student said at the sound of the bell after being introduced for the first time to the graphing calculator, "I finally learned something today." The teacher, Robert, thinks that such reactions can perhaps be explained by the technology-rich oriented society we live in today.
Many students, because they play with more complicated devices such
as Nintendo 64 or Play Station 2, are more than motivated to learn
mathematics concepts using the TI83 graphing calculator.
A point reinforced by Maria:
Students are so accustomed to playing with computer arcade games
that the technology tools become like toys. The solution resides in
an effective training of teachers toward the use of technology to
enhance mathematics learning.... It is almost a sin not to make use
of technology in the preparation of tomorrow's teachers and in the
classroom. It is regrettable that my district or school does not
provide graphing calculators, nor offers the training (Maria).
In addition, almost all teachers in both the course and workshops expressed this lack of administrative support. Most schools did not have a sufficient number of graphing calculators for all teachers to use at will. In some instances, teachers were not even aware that graphing calculators were available at their school. At the end of the last workshop, some PDS teachers, expressed their frustration not only about the lack of materials, but also about the lack of effective guidance on how to implement technology activities in the mathematics classroom.
This is fine information, but I wonder why are we spending time on
stuff we don't have, and I can't see when we'll have this stuff. We
need to focus on attainable goals and situations I suggest we get
trained on how to do things with little or no technology, because
that's where we are (John, from the workshops). Good crash course,
but the material relevant to 6th grade curriculum was not reviewed
(Christine, from the workshops).
Indeed, the workshops did not provide PDS teachers with time to design a plan for using suggested materials and methods in their classrooms. A long, sustained, and more coherent form of training would have provided more opportunities for active learning, and could have lead PDS teachers to report more favorably about their experience with technology. In contrast, because course participants were provided with more opportunities for active learning, they all reported a change in beliefs and attitudes toward the use of technology in the classroom, as evidenced by the comments.
In the past, I believed that using calculators was basically
cheating, because students didn't need to know how to find the
answer. They would just put the numbers in. I now believe this is a
good tool for students to see a lot of concepts. For example, a
class may only have time to graph 2 or 3 functions by hand, but if
a teacher wanted to show the effects that adding a constant to the
function or multiplying the function by a number might have, he/she
would want students to see more than just one or two examples.
Calculators can allow you to do that and help eliminate the time
factor (Judy from the course).
The technology tools used in this course have reinforced my belief
in the use of technology in the teaching of some mathematics
concepts. Because of the fact that most of our students are visual
learners and that the use of technology reduces the emphasis on
basic skills, the learner at this level can concentrate on the
concepts being developed. The graphing calculator provides a
laboratory approach to mathematics where students are given an
opportunity to take an active role in the development of their
knowledge base (Jean, from the course).
Teachers in the course, however, raised some additional concerns about the use of technology tools to teach mathematics. They called for prudence in designing curricular materials that use technology, by expressing concerns in the ability of the teacher to design effective lessons so that, when students are allowed to use calculators, they will not come to basically rely on them and lose the ability to think. The TI83 can certainly be a 'dangerous weapon' if one does not understand the mathematics (Robert). That is, teachers need to have the content background, and need to be trained effectively so to enable them to develop well-designed activities that are appropriate to students' levels of learning. APPENDIX A Attitude Questionnaire
Circle the number that best reflects your present attitude
0 Strongly Disagree 1 Disagree 2 Undecided 3 Agree 4 Strongly Agree
1. Calculators should "only" be used to check work. 0 1 2 3 4
2. A graphing calculator can be used as a tool to solve
problems I could not solve before. 0 1 2 3 4
3. Using a graphing calculator to teach mathematics or
science allows me to emphasize the experimental
nature of the subject. 0 1 2 3 4
4. Using a graphing calculator to teach math or science
does not enhance student learning or understanding of
concepts. 0 1 2 3 4
5. Learning mathematics is mostly memorizing a set of
facts and rules. 0 1 2 3 4
6. When doing mathematics, it is only important to know
how to do a process and not why it works. 0 1 2 3 4
7. Learning mathematics means exploring problems to
discover patterns and make generalizations. 0 1 2 3 4
8. I have difficulties gaining access to graphing
calculators for use in my classroom. 0 1 2 3 4
9. I have enough calculators for individual student use. 0 1 2 3 4
10. It is difficult to get funds to buy graphing
calculators. 0 1 2 3 4
11. My administration encourages use of graphing
calculators. 0 1 2 3 4
12. I lack confidence and skill with graphing
calculators. 0 1 2 3 4
13. Teaching with a graphing calculator is a high
priority in my department. 0 1 2 3 4
14. Students lack the ability to work with a calculator
as complex as a graphing calculator. 0 1 2 3 4
15. If students are taught to use technology, they will
come to rely on it and lose their ability to think. 0 1 2 3 4
Table 1 Comparison of the Pre- and Post-Survey Responses for Item 1
Item 1. Calculators should "only" be used to check work.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 1 3 2 4 2 2.25 1.29
(N=12) Post-Survey 6 5 0 1 0 .67 .89 1.58
PDS Pre-Survey 3 3 2 3 0 1.45 1.21
(N=11) Post-Survey 1 8 0 1 1 1.36 1.12 .1
Total Pre-Survey 4 6 4 7 2 1.87 1.29
(N=23) Post-Survey 7 13 0 2 1 1.00 1.04 .87
t p
Course Pre-Survey
(N=12) Post-Survey 3.50 .027*
PDS Pre-Survey
(N=11) Post-Survey .166 .871
Total Pre-Survey
(N=23) Post-Survey 2.30 .032*
* p<.05 significant
Table 2 Comparison of the Pre- and Post-Survey Responses for Item 2
Item 2. A graphing calculator can be used as a tool to solve problems
that I could not solve before.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 2 2 2 4 2 2.17 1.40
(N=12) Post-Survey 0 3 0 6 3 2.75 1.14 -.58
PDS Pre-Survey 1 0 3 4 3 2.73 1.19
(N=11) Post-Survey 1 1 2 3 4 2.73 1.35 0
Total Pre-Survey 3 2 5 8 5 2.43 1.31
(N=23) Post-Survey 1 4 2 9 7 2.74 1.21 -.30
t p
Course Pre-Survey
(N=12) Post-Survey -1.168 .267
PDS Pre-Survey
(N=11) Post-Survey 0 1.00
Total Pre-Survey
(N=23) Post-Survey -.850 .404
Table 3 Comparison of the Pre- and Post-Survey Responses for Item 3
Item 3. Using a graphing calculator to teach mathematics or science
allows me to emphasize the experimental nature of the subject.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 1 0 1 8 2 2.83 1.03
(N=12) Post-Survey 0 1 1 5 5 3.17 .94 .17
PDS Pre-Survey 0 0 5 4 2 2.73 .79
(N=11) Post-Survey 0 1 0 8 2 3.00 .77 -.27
Total Pre-Survey 1 0 6 12 4 2.78 .90
(N=23) Post-Survey 0 2 1 13 7 3.09 .85 .22
t p
Course Pre-Survey
(N=12) Post-Survey -.804 .438
PDS Pre-Survey
(N=11) Post-Survey -.896 .391
Total Pre-Survey
(N=23) Post-Survey -1.32 .200
Table 4 Comparison of the Pre- and Post-Survey Responses for Item 4
Item 4. Using a graphing calculator to teach math or science does not
enhance student learning or understanding of concepts.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 4 5 2 1 0 1.00 .95
(N=12) Post-Survey 6 6 0 0 0 .50 .52 .50
PDS Pre-Survey 6 2 1 1 0 .82 1.08
(N=11) Post-Survey 4 3 1 3 0 1.27 1.27 -.45
Total Pre-Survey 10 7 3 2 0 .91 1.00
(N=23) Post-Survey 10 9 1 3 0 .87 1.01 .04
t p
Course Pre-Survey
(N=12) Post-Survey 1.732 .111
PDS Pre-Survey
(N=11) Post-Survey -.922 .378
Total Pre-Survey
(N=23) Post-Survey .149 .883
Table 5 Comparison of the Pre- and Post-Survey Responses for Item 14
Item 14. Students lack the ability to work with a calculator as complex
as graphing calculator.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 0 3 2 4 3 2.58 1.16
(N=12) Post-Survey 7 0 3 1 1 1.08 1.44 1.50
PDS Pre-Survey 1 1 5 2 2 2.27 1.19
(N=11) Post-Survey 0 3 3 3 2 2.36 1.12 .1
Total Pre-Survey 1 4 7 6 5 2.43 1.16
(N=23) Post-Survey 7 3 6 4 3 1.70 1.43 .73
t p
Course Pre-Survey
(N=12) Post-Survey 2.292 .043*
PDS Pre-Survey
(N=11) Post-Survey -.219 .831
Total Pre-Survey
(N=23) Post-Survey 2.071 .05*
* p<.05 significant
Table 6 Comparison of the Pre- and Post-Survey Responses for Item 15
Item 15. If students are taught to use technology, they will come to
rely on it and lose their ability to think.
Rank Mean Standard Mean
0 1 2 3 4 Response Deviation Difference
Course Pre-Survey 1 6 1 1 3 1.92 1.44
(N=12) Post-Survey 3 6 1 1 1 1.25 1.01 .67
PDS Pre-Survey 1 4 3 3 0 1.73 1.01
(N=11) Post-Survey 3 3 3 1 1 1.45 1.29 .28
Total Pre-Survey 2 10 4 4 3 1.83 1.23
(N=23) Post-Survey 6 9 4 2 2 1.35 1.23 .48
t p
Course Pre-Survey
(N=12) Post-Survey .804 .438
PDS Pre-Survey
(N=11) Post-Survey .559 .588
Total Pre-Survey
(N=23) Post-Survey .369 .185
Acknowledgements I would like to thank Stan STAN Stanchion STAN Stärke- und Ausrüstungsnachweis (German) Stan Standard Man (human patient simulator) STAN SEMCIP Technical Assistance Network STAN System Trace Audit Number STAN Star Trek Area Network Taback, David Fletcher David Fletcher may refer to:
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