mathematics beliefs and teaching
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Questionnaire Interviews Introduction Participants’ beliefs concerning the nature of mathematics were approximately normally distributed around 2.5 indicating preservice teachers hold a mixture of absolutist and fallibilist beliefs (Figure 3). Preservice teachers indicated they intend to teach using a constructivist approach (Figure 4). Preservice teachers tend to fall into two categories when the alignment of their beliefs are examined (Figure 5). Preservice teachers who hold fallibilist beliefs about the nature of mathematics and intend to teach using a constructivist approach hold aligning beliefs. Preservice teachers who hold absolutist beliefs about the nature of mathematics and intend to teach using a constructivist approach hold apparently misaligning beliefs. Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics Teaching Faculty of Education, Queen’s University Sean Beaudette, Alexandra Penn & Geoffrey Roulet Preservice Teachers' Beliefs About the Nature of Mathematics and Effective Use of ICT On future use of Interactive Whiteboards (IWB): “Obviously not all kids are going to be into business where they would have to give presentations on it, but there are a lot of applications of it once they are out of school, or at least once they are in university” (David) vs. “I think the technology demands that we start using it in a more creative way” (Gary) Participants who demonstrated an absolutist belief about the nature of mathematics tended to focus on the IWB as a presentation tool. Comments focused on the size of the IWB, giving students in the class a better visual of what was happening at the front. Participants who demonstrated a fallibilist belief about the nature of mathematics generally had a deeper appreciation for the more advanced uses of IWBs, such as it’s use as a manipulative and the ability to save and open screens from past uses. This finding has implications for curriculum reform. Current curriculum documents suggest the use of constructivist instructional models and require the use of ICT in increasingly advanced ways. In recent years, EQAO scores have suggested that teachers are following these directives. However, this may not be the case in mathematics. The results of this study show that if one has an absolutist belief about the nature of mathematics, they may be more likely to value ICT as a tool used to transfer knowledge from expert to novice. Results & Discussion Future Directions & Acknowledgements The Apparent Misalignment of Preservice Teachers' Beliefs About the Nature of Mathematics and Teaching and Learning in Terms of Intended Manipulative Use When the nature of mathematics was discussed, preservice teachers were found to hold a mixture of both absolutist and fallibilist beliefs about the nature of mathematics, however many held more absolute beliefs. All participants spoke of using manipulates to support a constructivist approach. This included using manipulatives during group work and using manipulatives to assist students explore problems and discuss their ideas. However, when the intended use of manipulatives was explored in more detail a more traditional teaching approach emerged. For example manipulatives were used during group work to make math fun and to check to make sure students had the right process and product. When asked how she would help a struggling student, Julie responded, “I would probably spend a little bit of time with her and explain the process still using the block, borrowing like the way I did it in my lesson. Ok what does 26 look like, what does 7 look like and how you would place it or what 17 looks like and how you would place it. And then I would visually show her so that she was still using the blocks, it was still fun” The use of manipulatives is often used as an indicator that the constructivist approach is being employed; however how the manipulatives are being used is often not taken into account. While the preservice teachers indicated that they do intend to use manipulatives in their future teaching, there is evidence that they intend to use manipulatives to support a traditional approach to teaching mathematics. This suggests their beliefs about mathematics do align with how they intend to teach. Teachers’ beliefs about mathematics and instruction of mathematics are important and influence teachers’ enacted instructional practices (Brown & Cooney, 1982; Pajares, 1992; Richardson, 1996). Even before starting their first courses in education, preservice teachers hold a wide range of beliefs about mathematics, as well as beliefs about teaching mathematics (Ball, 1988). Beliefs concerning the nature of mathematics can be roughly divided into two epistemological positions, absolutist and fallibilist (Figure 1). Beliefs concerning the teaching and learning of mathematics can be roughly divided into two approaches, traditional and constructivist (Figure 2). It has been shown that teachers with absolutist views of mathematics tend to follow a traditional instructional model while teachers with fallibilist views often use a constructivist approach (Chan, 2011; Chan & Elliott, 2004; Crissan, Lerman & Winbourne, 2007; Yadav & Koehler, 2007). On the other hand, some teachers holding absolutist views do employ concrete manipulatives and information communication technology (ICT) in their instruction (Judson, 2006, Liljedahl, Rösken & Rolka, 2006), two actions promoted by the mathematics reform movement and rooted in a constructivist view of the subject (Romberg, 1992). Data collection began one month prior to the commencement of classes in the 2011-2012 school year and extended into the first two weeks of term. The study had three parts. A questionnaire was used to gain a general understanding of how beliefs regarding the nature of mathematics and the teaching of mathematics are represented in preservice elementary teachers at Queen’s University. This data was used to select participants for two separate interview-based research projects. Two separate sets of interview took place with volunteers who identified themselves as willing participants through the questionnaire. The interviews were used to triangulate the results of the questionnaire and allow further exploration of manipulative and ICT use. One set of interviews focused on participants with opposing beliefs about the nature of mathematics and how those beliefs relate to ICT use in the classroom. The second set of interviews examined the alignment of teachers’ beliefs concerning the nature of mathematics and mathematics teaching through the use of manipulatives. All interviews were be semi-structured, lasted approximately one hour, and were audio-recorded. The interview transcripts were analyzed qualitatively using ATLAS-ti ® analysis software in order to allow topics, categories and patterns to emerge from data. Method Given the importance of teachers’ beliefs, the purpose of this study was to document and examine the beliefs concerning the nature of mathematics and perceived effective mathematics instruction held by preservice elementary teachers prior to entering a teacher education program Purpose We would like to thank Dr. Richard Reeve, Dr. Jamie Pyper, and the Faculty of Education at Queen’s University. This research adds to the body of knowledge concerning preservice teachers’ beliefs about the nature of mathematics and intended instructional practices. The findings of this study may impact teacher education programs . It would be valuable to conduct future research of this nature over the course of an entire B. Ed. year with the aim of examining potential change in participant beliefs.
Transcript of mathematics beliefs and teaching
Questionnaire
Interviews
IntroductionParticipants’ beliefs concerning the nature of mathematics were approximately normally distributed around 2.5 indicating preservice teachers hold a mixture of absolutist and fallibilistbeliefs (Figure 3). Preservice teachers indicated they intend to teach using a constructivist approach (Figure 4). Preservice teachers tend to fall into two categories when the alignmentof their beliefs are examined (Figure 5). Preservice teachers who hold fallibilist beliefs about the nature of mathematics and intend to teach using a constructivist approach hold aligningbeliefs. Preservice teachers who hold absolutist beliefs about the nature of mathematics and intend to teach using a constructivist approach hold apparently misaligning beliefs.
Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics TeachingFaculty of Education, Queen’s UniversitySean Beaudette, Alexandra Penn & Geoffrey Roulet
Preservice Teachers' Beliefs About the Nature of Mathematics and Effective Use of ICT
On future use of Interactive Whiteboards (IWB):“Obviously not all kids are going to be into business where they would have to givepresentations on it, but there are a lot of applications of it once they are out ofschool, or at least once they are in university” (David)
vs.“I think the technology demands that we start using it in a more creative way”(Gary)
Participants who demonstrated an absolutist belief about the nature of mathematicstended to focus on the IWB as a presentation tool. Comments focused on the size ofthe IWB, giving students in the class a better visual of what was happening at thefront.
Participants who demonstrated a fallibilist belief about the nature of mathematicsgenerally had a deeper appreciation for the more advanced uses of IWBs, such as it’suse as a manipulative and the ability to save and open screens from past uses.
This finding has implications for curriculum reform. Current curriculumdocuments suggest the use of constructivist instructional models and require the useof ICT in increasingly advanced ways. In recent years, EQAO scores have suggestedthat teachers are following these directives. However, this may not be the case inmathematics. The results of this study show that if one has an absolutist belief aboutthe nature of mathematics, they may be more likely to value ICT as a tool used totransfer knowledge from expert to novice.
Results & Discussion
Future Directions & Acknowledgements
The Apparent Misalignment of Preservice Teachers' Beliefs About the Nature of Mathematics and Teaching and Learning in
Terms of Intended Manipulative UseWhen the nature of mathematics was discussed, preservice teachers were found to hold a mixtureof both absolutist and fallibilist beliefs about the nature of mathematics, however many heldmore absolute beliefs.
All participants spoke of using manipulates to support a constructivist approach. This includedusing manipulatives during group work and using manipulatives to assist students exploreproblems and discuss their ideas. However, when the intended use of manipulatives was exploredin more detail a more traditional teaching approach emerged. For example manipulatives wereused during group work to make math fun and to check to make sure students had the rightprocess and product.
When asked how she would help a struggling student, Julie responded, “I would probably spend alittle bit of time with her and explain the process still using the block, borrowing like the way I didit in my lesson. Ok what does 26 look like, what does 7 look like and how you would place it orwhat 17 looks like and how you would place it. And then I would visually show her so that shewas still using the blocks, it was still fun”
The use of manipulatives is often used as an indicator that the constructivist approach is beingemployed; however how the manipulatives are being used is often not taken into account. Whilethe preservice teachers indicated that they do intend to use manipulatives in their futureteaching, there is evidence that they intend to use manipulatives to support a traditionalapproach to teaching mathematics. This suggests their beliefs about mathematics do align withhow they intend to teach.
Teachers’ beliefs about mathematics and instruction of mathematics are important and influenceteachers’ enacted instructional practices (Brown & Cooney, 1982; Pajares, 1992; Richardson, 1996).Even before starting their first courses in education, preservice teachers hold a wide range ofbeliefs about mathematics, as well as beliefs about teaching mathematics (Ball, 1988). Beliefsconcerning the nature of mathematics can be roughly divided into two epistemological positions,absolutist and fallibilist (Figure 1). Beliefs concerning the teaching and learning of mathematics canbe roughly divided into two approaches, traditional and constructivist (Figure 2). It has beenshown that teachers with absolutist views of mathematics tend to follow a traditional instructionalmodel while teachers with fallibilist views often use a constructivist approach (Chan, 2011; Chan &Elliott, 2004; Crissan, Lerman & Winbourne, 2007; Yadav & Koehler, 2007). On the other hand,some teachers holding absolutist views do employ concrete manipulatives and informationcommunication technology (ICT) in their instruction (Judson, 2006, Liljedahl, Rösken & Rolka,2006), two actions promoted by the mathematics reform movement and rooted in a constructivistview of the subject (Romberg, 1992).
Data collection began one month prior to the commencement of classes in the 2011-2012 schoolyear and extended into the first two weeks of term. The study had three parts. A questionnairewas used to gain a general understanding of how beliefs regarding the nature of mathematics andthe teaching of mathematics are represented in preservice elementary teachers at Queen’sUniversity. This data was used to select participants for two separate interview-based researchprojects.
Two separate sets of interview took place with volunteers who identified themselves as willingparticipants through the questionnaire. The interviews were used to triangulate the results of thequestionnaire and allow further exploration of manipulative and ICT use. One set of interviewsfocused on participants with opposing beliefs about the nature of mathematics and how thosebeliefs relate to ICT use in the classroom. The second set of interviews examined the alignment ofteachers’ beliefs concerning the nature of mathematics and mathematics teaching through the useof manipulatives. All interviews were be semi-structured, lasted approximately one hour, andwere audio-recorded. The interview transcripts were analyzed qualitatively using ATLAS-ti®
analysis software in order to allow topics, categories and patterns to emerge from data.
Method
Given the importance of teachers’ beliefs, the purpose of this study was to document and examine the beliefs concerning the nature of mathematics and perceived effective mathematics instruction held by preservice elementary teachers prior to entering a teacher education program
Purpose
We would like to thank Dr. Richard Reeve, Dr. Jamie Pyper, and the Faculty of Education at Queen’s University.
This research adds to the body of knowledge concerning preservice teachers’ beliefs about the nature of mathematics and intended instructional practices. The findings of this study may impact teacher education programs . It would be valuable to conduct future research of this nature over the course of an entire B. Ed. year with the aim of examining potential change in participant beliefs.
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