Framing Issues Paper
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MATH EDUCATION AND ICT INTEGRATION: SITUATING ATTITUDE AND PERCEPTION IN PRACTICE
Nancy Castonguay 58677980
ETEC 533 - Technology in the Mathematics and Science Classroom Section 65 A Dr. Samia Khan 15 February 2009
Constructivists assert that effective learning occurs when learners are actively involved in the construction of knowledge as opposed to being taught via traditional one-way instruction. What is more, active learning requires a space in which learners can manipulate, discuss and interpret information in context; a space in which they can apply newly constructed knowledge immediately by performing authentic tasks. ICT (this term will be used throughout to refer to the use of Web tools and may also be interchanged with the term ‘new technology’), if anchored in sound instructional design, can provide learners with the space and the tools they need to engage in discovery learning. (Ally, 2004, ¶ 28-31) Unfortunately, ICT use is not the norm in most faceto-face math education programs. In the winter of 2009, MET (Master of Educational Technology Program - UBC) students conducted a series of interviews with K-12 math and science teachers (mostly in located in Canada) to get a better grasp on current issues relating to the use of new ICT in those subject areas. The interviews re-iterated what already is common knowledge in education: the main reasons teachers don’t use ICT in their classrooms are the lack of access to new technology, the lack of expertise, and the lack of time. This void of rudimentary resources, combined with the uncertainty that taking the steps (and sometimes leaps) necessary to integrate ICT into the curriculum will have a lasting and positive effect on learning, affects teacher’s attitude toward ICT integration. Specific to math education and adding to the challenge is that math teachers have to content with outdated notions that math education requires not the use of technology to be effective. The focus of this paper then, is to explore the impact of attitude and perception on the use of ICT in the K-12 math classroom, but because attitude affects all teachers, it will be discussed as such.
Oriel Kelly (2007) uses the metaphor of introducing a vacuum cleaner to a room full of cats to highlight the various attitudes teachers have toward new technologies (Kelly, 2007). There are those who high tail it out the cat door, and you never see them again. There are those who do not show such obvious fear, but who walk sedately away, with great dignity, muttering, “That is all very interesting but I really don’t have time for that sort of thing.” There are those who leap straight to the highest vantage point they can find and criticize loudly from their lofty position about how it is a dreadful thing and would never work for their subject area anyway. There are those who hunker down, shut their eyes, and pretend it isn’t happening, because “It, too, shall pass.” There are those who initially take refuge behind the nearest piece of furniture, but peer out, mildly interested. They can probably be enticed to play, once it is well established that it’s safe to do so and that they will not be in great danger after all. And then there are those who come straight up – who want to play with it, embrace it, and are very willing to go along for the ride, wherever it takes them. (p. 35)
Although Kelly’s discussion is centered on selling the idea of ICT integration to faculty in higher education, his ideas apply to the K-12 environment. Kelly argues that the integration of ICT in education meets resistance at various levels, as described above. This is in part because integrating ICT into instructional design often means letting go of some control in the classroom, changing one’s role from instructor to facilitator. Resistance is also related to the fact that skill level with ICT varies from teacher to teacher; everyone is at a different starting point. Kelly explains that the overwhelming feeling experienced by some could be alleviated by exploring the various degrees to which ICT can be integrated. That is to say that very small change in practice can build confidence and still achieve positive results. But he also stresses that in order for mindset to be shifted, several things must happen. Teachers need to know that they will receive the support needed, and more importantly, the training required to achieve purposeful integration of ICT in the classroom based on a constructivist approach. Most of all, teachers need to be convinced that using new technologies in the classroom will have a deep and long-lasting impact on learning (Kelly, 2007, p.45).
Studies on the effectiveness of ICT in education can add to the confusion. Cuban & Kirkpatrick (1998) contend that much of the literature related to the effectiveness of computerenhanced learning is questionable for several reasons. First, single studies are seldom unbiased and often neglect to disclose relevant factors such as environmental variables. Meta-analyses tend to only include single studies that will support a favorable outcome. Not surprisingly, most critical reviews of meta-analyses and single studies have found several flaws such as those relating to sample size or study length. Moreover, studies that are favorable to computerenhanced learning never seem to be clear about whether or not higher scores can be attributed to enhanced short-term memory or whether they came as a of enhanced critical thinking (Cuban & Kilpatrick, 1998, pp. 26-28). As Ally (2004) stresses, computers alone cannot engender active learning; ICT must be anchored in solid instructional design in order to be effective. However, Niess (2006) contends that most teachers are ill equipped to integrate ICT in learning and teaching. In the case of math education, she suggests that student teachers and their instructors “have at best a limited knowledge of potential technologies for use in mathematics” (Niess, 2006, ¶ 9). Especially for those teachers who have been around the block a few times, the argument for technology integration begins to look more and more like quick sand than sound educational reform. In math education, the buy-in process for ICT use in the classroom is further complicated by archaic perceptions. Chirico (2009), a secondary school math teacher, contends that the technology issue in math education is in fact deeply rooted in generalizations about math. Math is stereotyped as a boring subject and the common belief is that this is how it has to be. The complete math experience has not likely changed much since I was in my first year of Calculus in 2000: arrive, sit, copy notes, ask questions if you understand enough of what’s going on, flee
to some dark corner of the library in the hopes that you’ll be able to make sense of your notes by looking at other examples in textbooks, cross your fingers, wipe your forehead, remind yourself that after all, Calculus is the art of approximation, go back and take the test. Seems perfectly normal, right? If you nodded your head indicating that the answer is ‘yes’, then you too are perpetuating the perception that math education consists merely in the mastery of a body of knowledge and a set of techniques.
This perception of math education makes the acquisition of new technologies and the use of ICT in the math classroom futile. Chirico’s testimony illustrates this precisely as she states that requests to purchase new technology for the math department at her school are generally denied because the administration “[does] not see a need in ‘fancying’ up how we teach math”. Apparently, math teachers should find themselves lucky to have access to LCD projectors, which were installed in classrooms for purposes other than math education (Chirico, 2009). What is more, perceptions about how math should be taught affect math teachers’ access to the school’s computer lab since it is generally reserved for other, seemingly needier subject areas. “[No] one takes students into a lab … There is no labe (sic) that we could gain access to” (Chirico, 2009). Overall, math education is not perceived as a subject area that could benefit from the use of ICT.
Archaic perceptions about math education are not limited to people who do not understand mathematics, math teachers also contribute to perpetuating the cycle. According to Furinghetti (2007), math education is influenced by 3 distinct forces: the teacher's knowledge of the subject, pedagogical knowledge, and preconceived beliefs about how math should be taught. Furinghetti argues that math teachers generally teach math the same way they were taught it in school. Furthermore, the evidence he collected suggests that teachers find it difficult to even
think about teaching math any other way. Furinghetti contends that, as a result of these deeply rooted beliefs, teachers are more likely to reject any attempts at reforming math education. Unconsciously, teachers who have not been trained to find their own “aware way of teaching” math fall victim to the generations of mathematicians who "have no interest in looking below the instrumental or formal surface of mathematics in order to get clues about how to present it more effectively" (Furinghetti, 2007, p. 132). Furinghetti proposes that reforming teacher education is central to reforming math education. In a study he conducted, a math history course was incorporated to the teacher training curriculum and this positively influenced new math teachers' beliefs about math education. Going back in time allowed teachers to challenge their own perceptions about math; they reflected on how concepts were engendered in mathematics. By studying the history of mathematics, new teachers demonstrated in their lesson planning that they were not limited to identifying the concepts needed to solve problems; they were also aware of the skills required to develop them, for example, the cognitive roots of algebra. The experimental teacher education curriculum forced teachers to experience the construction math objects which later enabled them to develop their own awareness about how mathematical knowledge was constructed (Furinghetti, 2007, pp. 131-143). Again, what is important to remember is that teaching new teachers about new technologies and how to use them is not enough to have any effect on math education. Central to reforming minds about math education and about attitudes surrounding ICT in the math classroom is the training of new educators in technology integration (Mistretta, 2005). There is no quick fix to shifting minds and altering perceptions, but clearly, teacher education reform is a step in the right direction. In order for students to change their views on
math education, math programs must cross over into the 21st century. Math education need not to feel like a visit at the dentist or bootcamp for the Spelling Bee; new technologies could be used to make each math lesson feel more like a field trip. The inability of math teachers to make a strong argument for technology in math education affects technology spending and allocation. Coming back to my interview with Chirico, math teachers do want to try new things but they often lack the tools and the expertise to do so. Initiatives are weighed down by pervasive attitudes that could be overcome, as it was the case in Mistretta’s study where 70 teachers experienced a complete turn-around in thinking about technology education in the math classroom (Mistretta, 2005, p.22). And archaic perceptions of math education would quickly dissipate if math teachers were only given he chance to experiment with more technology.
References Ally, Mohamed. (2004). Foundations of educational theory for online learning. In Anderson, T. & Elloumi, F. (Eds.), Theory and Practice of Online Learning (chapter 1). Retrieved from http://cde.athabascau.ca/online_book/ch1.html Castonguay, N. & Chirico, S. (2009). Situating attitude in practice [Interview transcript]. Retrieved from http://recordings.dimdim.com/chat/dimdim/dc8975ee-3ca4-102c-bbd7003048944478 Cuban, Larry & Kirkpatrick, Heather. (1998). Computers make kids smarter – Right? Technos, 7 (2), pp. 28-31. Furinghetti, Fulvia. (2007). Teacher education throught the history of mathematics. Educational Studies in Mathematics, 66 (2), pp. 131-143. Retrieved from http://www.springerlink.com/index/X557561943K81JM7.pdf Bass, Hyman. (2005). Mathematics, mathematicians, and mathematics education. Bulletin New Series of the American Mathematical Society, 42 (4), pp. 417-430. Retrieved from http://www.ams.org/bull/2005-42-04/S0273-0979-05-01072-4/S0273-0979-05-010724.pdf Kelly, Oriel. (2007). Moving to blended delivery in a polytechnic: Shifting the mindset of faculty and institutions. In M. Bullen & D.P. Janes (Eds.), Making the Transition to E-Learning: Strategies and Issues (pp. 33-45). Hershey, PA: Information Science Publishing.
Mistretta, Regina M. (2005). Integrating technology into the mathematics classroom: The role of teacher preparation programs. The Mathematics Educator, 15(1), pp. 18-24. Niess, Margaret L. (2006). Preparing teachers to teach mathematics with technology. Retrieved from http://site.aace.org/pubs/foresite/MathematicsEd.pdf
Nancy Castonguay 58677980
ETEC 533 - Technology in the Mathematics and Science Classroom Section 65 A Dr. Samia Khan 15 February 2009
Constructivists assert that effective learning occurs when learners are actively involved in the construction of knowledge as opposed to being taught via traditional one-way instruction. What is more, active learning requires a space in which learners can manipulate, discuss and interpret information in context; a space in which they can apply newly constructed knowledge immediately by performing authentic tasks. ICT (this term will be used throughout to refer to the use of Web tools and may also be interchanged with the term ‘new technology’), if anchored in sound instructional design, can provide learners with the space and the tools they need to engage in discovery learning. (Ally, 2004, ¶ 28-31) Unfortunately, ICT use is not the norm in most faceto-face math education programs. In the winter of 2009, MET (Master of Educational Technology Program - UBC) students conducted a series of interviews with K-12 math and science teachers (mostly in located in Canada) to get a better grasp on current issues relating to the use of new ICT in those subject areas. The interviews re-iterated what already is common knowledge in education: the main reasons teachers don’t use ICT in their classrooms are the lack of access to new technology, the lack of expertise, and the lack of time. This void of rudimentary resources, combined with the uncertainty that taking the steps (and sometimes leaps) necessary to integrate ICT into the curriculum will have a lasting and positive effect on learning, affects teacher’s attitude toward ICT integration. Specific to math education and adding to the challenge is that math teachers have to content with outdated notions that math education requires not the use of technology to be effective. The focus of this paper then, is to explore the impact of attitude and perception on the use of ICT in the K-12 math classroom, but because attitude affects all teachers, it will be discussed as such.
Oriel Kelly (2007) uses the metaphor of introducing a vacuum cleaner to a room full of cats to highlight the various attitudes teachers have toward new technologies (Kelly, 2007). There are those who high tail it out the cat door, and you never see them again. There are those who do not show such obvious fear, but who walk sedately away, with great dignity, muttering, “That is all very interesting but I really don’t have time for that sort of thing.” There are those who leap straight to the highest vantage point they can find and criticize loudly from their lofty position about how it is a dreadful thing and would never work for their subject area anyway. There are those who hunker down, shut their eyes, and pretend it isn’t happening, because “It, too, shall pass.” There are those who initially take refuge behind the nearest piece of furniture, but peer out, mildly interested. They can probably be enticed to play, once it is well established that it’s safe to do so and that they will not be in great danger after all. And then there are those who come straight up – who want to play with it, embrace it, and are very willing to go along for the ride, wherever it takes them. (p. 35)
Although Kelly’s discussion is centered on selling the idea of ICT integration to faculty in higher education, his ideas apply to the K-12 environment. Kelly argues that the integration of ICT in education meets resistance at various levels, as described above. This is in part because integrating ICT into instructional design often means letting go of some control in the classroom, changing one’s role from instructor to facilitator. Resistance is also related to the fact that skill level with ICT varies from teacher to teacher; everyone is at a different starting point. Kelly explains that the overwhelming feeling experienced by some could be alleviated by exploring the various degrees to which ICT can be integrated. That is to say that very small change in practice can build confidence and still achieve positive results. But he also stresses that in order for mindset to be shifted, several things must happen. Teachers need to know that they will receive the support needed, and more importantly, the training required to achieve purposeful integration of ICT in the classroom based on a constructivist approach. Most of all, teachers need to be convinced that using new technologies in the classroom will have a deep and long-lasting impact on learning (Kelly, 2007, p.45).
Studies on the effectiveness of ICT in education can add to the confusion. Cuban & Kirkpatrick (1998) contend that much of the literature related to the effectiveness of computerenhanced learning is questionable for several reasons. First, single studies are seldom unbiased and often neglect to disclose relevant factors such as environmental variables. Meta-analyses tend to only include single studies that will support a favorable outcome. Not surprisingly, most critical reviews of meta-analyses and single studies have found several flaws such as those relating to sample size or study length. Moreover, studies that are favorable to computerenhanced learning never seem to be clear about whether or not higher scores can be attributed to enhanced short-term memory or whether they came as a of enhanced critical thinking (Cuban & Kilpatrick, 1998, pp. 26-28). As Ally (2004) stresses, computers alone cannot engender active learning; ICT must be anchored in solid instructional design in order to be effective. However, Niess (2006) contends that most teachers are ill equipped to integrate ICT in learning and teaching. In the case of math education, she suggests that student teachers and their instructors “have at best a limited knowledge of potential technologies for use in mathematics” (Niess, 2006, ¶ 9). Especially for those teachers who have been around the block a few times, the argument for technology integration begins to look more and more like quick sand than sound educational reform. In math education, the buy-in process for ICT use in the classroom is further complicated by archaic perceptions. Chirico (2009), a secondary school math teacher, contends that the technology issue in math education is in fact deeply rooted in generalizations about math. Math is stereotyped as a boring subject and the common belief is that this is how it has to be. The complete math experience has not likely changed much since I was in my first year of Calculus in 2000: arrive, sit, copy notes, ask questions if you understand enough of what’s going on, flee
to some dark corner of the library in the hopes that you’ll be able to make sense of your notes by looking at other examples in textbooks, cross your fingers, wipe your forehead, remind yourself that after all, Calculus is the art of approximation, go back and take the test. Seems perfectly normal, right? If you nodded your head indicating that the answer is ‘yes’, then you too are perpetuating the perception that math education consists merely in the mastery of a body of knowledge and a set of techniques.
This perception of math education makes the acquisition of new technologies and the use of ICT in the math classroom futile. Chirico’s testimony illustrates this precisely as she states that requests to purchase new technology for the math department at her school are generally denied because the administration “[does] not see a need in ‘fancying’ up how we teach math”. Apparently, math teachers should find themselves lucky to have access to LCD projectors, which were installed in classrooms for purposes other than math education (Chirico, 2009). What is more, perceptions about how math should be taught affect math teachers’ access to the school’s computer lab since it is generally reserved for other, seemingly needier subject areas. “[No] one takes students into a lab … There is no labe (sic) that we could gain access to” (Chirico, 2009). Overall, math education is not perceived as a subject area that could benefit from the use of ICT.
Archaic perceptions about math education are not limited to people who do not understand mathematics, math teachers also contribute to perpetuating the cycle. According to Furinghetti (2007), math education is influenced by 3 distinct forces: the teacher's knowledge of the subject, pedagogical knowledge, and preconceived beliefs about how math should be taught. Furinghetti argues that math teachers generally teach math the same way they were taught it in school. Furthermore, the evidence he collected suggests that teachers find it difficult to even
think about teaching math any other way. Furinghetti contends that, as a result of these deeply rooted beliefs, teachers are more likely to reject any attempts at reforming math education. Unconsciously, teachers who have not been trained to find their own “aware way of teaching” math fall victim to the generations of mathematicians who "have no interest in looking below the instrumental or formal surface of mathematics in order to get clues about how to present it more effectively" (Furinghetti, 2007, p. 132). Furinghetti proposes that reforming teacher education is central to reforming math education. In a study he conducted, a math history course was incorporated to the teacher training curriculum and this positively influenced new math teachers' beliefs about math education. Going back in time allowed teachers to challenge their own perceptions about math; they reflected on how concepts were engendered in mathematics. By studying the history of mathematics, new teachers demonstrated in their lesson planning that they were not limited to identifying the concepts needed to solve problems; they were also aware of the skills required to develop them, for example, the cognitive roots of algebra. The experimental teacher education curriculum forced teachers to experience the construction math objects which later enabled them to develop their own awareness about how mathematical knowledge was constructed (Furinghetti, 2007, pp. 131-143). Again, what is important to remember is that teaching new teachers about new technologies and how to use them is not enough to have any effect on math education. Central to reforming minds about math education and about attitudes surrounding ICT in the math classroom is the training of new educators in technology integration (Mistretta, 2005). There is no quick fix to shifting minds and altering perceptions, but clearly, teacher education reform is a step in the right direction. In order for students to change their views on
math education, math programs must cross over into the 21st century. Math education need not to feel like a visit at the dentist or bootcamp for the Spelling Bee; new technologies could be used to make each math lesson feel more like a field trip. The inability of math teachers to make a strong argument for technology in math education affects technology spending and allocation. Coming back to my interview with Chirico, math teachers do want to try new things but they often lack the tools and the expertise to do so. Initiatives are weighed down by pervasive attitudes that could be overcome, as it was the case in Mistretta’s study where 70 teachers experienced a complete turn-around in thinking about technology education in the math classroom (Mistretta, 2005, p.22). And archaic perceptions of math education would quickly dissipate if math teachers were only given he chance to experiment with more technology.
References Ally, Mohamed. (2004). Foundations of educational theory for online learning. In Anderson, T. & Elloumi, F. (Eds.), Theory and Practice of Online Learning (chapter 1). Retrieved from http://cde.athabascau.ca/online_book/ch1.html Castonguay, N. & Chirico, S. (2009). Situating attitude in practice [Interview transcript]. Retrieved from http://recordings.dimdim.com/chat/dimdim/dc8975ee-3ca4-102c-bbd7003048944478 Cuban, Larry & Kirkpatrick, Heather. (1998). Computers make kids smarter – Right? Technos, 7 (2), pp. 28-31. Furinghetti, Fulvia. (2007). Teacher education throught the history of mathematics. Educational Studies in Mathematics, 66 (2), pp. 131-143. Retrieved from http://www.springerlink.com/index/X557561943K81JM7.pdf Bass, Hyman. (2005). Mathematics, mathematicians, and mathematics education. Bulletin New Series of the American Mathematical Society, 42 (4), pp. 417-430. Retrieved from http://www.ams.org/bull/2005-42-04/S0273-0979-05-01072-4/S0273-0979-05-010724.pdf Kelly, Oriel. (2007). Moving to blended delivery in a polytechnic: Shifting the mindset of faculty and institutions. In M. Bullen & D.P. Janes (Eds.), Making the Transition to E-Learning: Strategies and Issues (pp. 33-45). Hershey, PA: Information Science Publishing.
Mistretta, Regina M. (2005). Integrating technology into the mathematics classroom: The role of teacher preparation programs. The Mathematics Educator, 15(1), pp. 18-24. Niess, Margaret L. (2006). Preparing teachers to teach mathematics with technology. Retrieved from http://site.aace.org/pubs/foresite/MathematicsEd.pdf
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