Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem solving into inclusive classrooms, in which some students may struggle with the self-regulation skills involved in problem solving, can be challenging. This article offers several problem solving procedures, as well as examples of problem solving in the classroom, that can provide young children with learning disabilities the support they need to meaningfully engage in mathematical problem solving.
{"title":"Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom.","authors":"Nicole Fletcher","doi":"10.7916/JMETC.V5I1.642","DOIUrl":"https://doi.org/10.7916/JMETC.V5I1.642","url":null,"abstract":"Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem solving into inclusive classrooms, in which some students may struggle with the self-regulation skills involved in problem solving, can be challenging. This article offers several problem solving procedures, as well as examples of problem solving in the classroom, that can provide young children with learning disabilities the support they need to meaningfully engage in mathematical problem solving.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"5 1","pages":"41-46"},"PeriodicalIF":0.0,"publicationDate":"2014-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the Order of Operations and the effectiveness of a new approach.
{"title":"Exploring Mathematical Reasoning of the Order of Operations: Rearranging the Procedural Component PEMDAS","authors":"J. Lee, Susan Licwinko, Nicole Taylor-Buckner","doi":"10.7916/JMETC.V4I2.633","DOIUrl":"https://doi.org/10.7916/JMETC.V4I2.633","url":null,"abstract":"PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the Order of Operations and the effectiveness of a new approach.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":"73-78"},"PeriodicalIF":0.0,"publicationDate":"2013-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak’s 25 years of service to the school. This article is adapted from my talk at this conference covering Mathematical Modeling in the Common Core, what it means for educators as we move toward this future reality, and what we can do to succeed in this brave new world.
{"title":"Slides from Dr. Schoenfeld's Talk","authors":"A. Schoenfeld","doi":"10.7916/JMETC.V4I2.622","DOIUrl":"https://doi.org/10.7916/JMETC.V4I2.622","url":null,"abstract":"On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak’s 25 years of service to the school. This article is adapted from my talk at this conference covering Mathematical Modeling in the Common Core, what it means for educators as we move toward this future reality, and what we can do to succeed in this brave new world.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering why developing creativity is a worthwhile adventure for students; describing why collaborative problem solving is a unique endeavor in which to engage students more fluidly and less compartmentally; and discussing how students can become skilled at thinking logically and creatively about mathematics content through their engagement in collaborative problem solving tasks.
{"title":"Developing Creativity Through Collaborative Problem Solving","authors":"Lillie R. Albert, Rina Kim","doi":"10.7916/JMETC.V4I2.627","DOIUrl":"https://doi.org/10.7916/JMETC.V4I2.627","url":null,"abstract":"This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering why developing creativity is a worthwhile adventure for students; describing why collaborative problem solving is a unique endeavor in which to engage students more fluidly and less compartmentally; and discussing how students can become skilled at thinking logically and creatively about mathematics content through their engagement in collaborative problem solving tasks.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":"32-38"},"PeriodicalIF":0.0,"publicationDate":"2013-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for Research in Mathematics (CERME), particularly in the last few years. The aim of the article is to show the similarities and the differences in the teaching and learning of mathematical modelling within education in Europe.
{"title":"Mathematical Modelling in European Education.","authors":"R. Ferri","doi":"10.7916/JMETC.V4I2.624","DOIUrl":"https://doi.org/10.7916/JMETC.V4I2.624","url":null,"abstract":"Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for Research in Mathematics (CERME), particularly in the last few years. The aim of the article is to show the similarities and the differences in the teaching and learning of mathematical modelling within education in Europe.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":"18-24"},"PeriodicalIF":0.0,"publicationDate":"2013-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathematical Modeling has recently become a compulsory part of the Common Core State Standards (CCSS) in the United States. Future teachers must have a strong background about different aspects of modeling and also about appropriate methods for how modeling can be taught. In which ways modeling is the teacher’s responsibility is presented in this paper on the basis of theoretical reflections as well as an in depth focus on more practical experiences and results of empirical studies of pre- and in-service teacher education. Finally a model of necessary teaching competencies for modeling is described in the four dimensions and a conclusion is drawn.
{"title":"Mathematical Modeling—The Teacher’s Responsibility","authors":"R. Ferri","doi":"10.7916/JMETC.V0I0.660","DOIUrl":"https://doi.org/10.7916/JMETC.V0I0.660","url":null,"abstract":"Mathematical Modeling has recently become a compulsory part of the Common Core State Standards (CCSS) in the United States. Future teachers must have a strong background about different aspects of modeling and also about appropriate methods for how modeling can be taught. In which ways modeling is the teacher’s responsibility is presented in this paper on the basis of theoretical reflections as well as an in depth focus on more practical experiences and results of empirical studies of pre- and in-service teacher education. Finally a model of necessary teaching competencies for modeling is described in the four dimensions and a conclusion is drawn.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak’s 25 years of service to the school. This article is adapted from my talk at this conference covering Mathematical Modeling in the Common Core, what it means for educators as we move toward this future reality, and what we can do to succeed in this brave new world.
{"title":"Mathematical Modeling, Sense Making, and the Common Core State Standards.","authors":"A. Schoenfeld","doi":"10.7916/JMETC.V0I0.659","DOIUrl":"https://doi.org/10.7916/JMETC.V0I0.659","url":null,"abstract":"On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak’s 25 years of service to the school. This article is adapted from my talk at this conference covering Mathematical Modeling in the Common Core, what it means for educators as we move toward this future reality, and what we can do to succeed in this brave new world.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":"6-17"},"PeriodicalIF":0.0,"publicationDate":"2013-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathematical Modeling is being introduced as a new product into the complex system of Mathematics Education. It has to fit with the existing parts and interfaces in this system. As one example, we will consider the effect of mathematical modeling on the transition from secondary to tertiary education. If mathematical modeling is of greater importance to the planners at one of these two levels of education than at the other, then stresses may result. As a second example, we propose to examine changes in teacher education necessitated by the introduction of mathematical modeling at the secondary level. Ideally, one might wish to prepare teachers to teach mathematical modeling by concentrating purely on modeling without the distraction of new mathematical ideas, but it is not clear that this can always be done. Finally, we plan to make some comments on the effect of mathematical modeling has on the relationship between mathematics education and mathematics itself. Each of these should gain from cooperation with the other.
{"title":"A View of Mathematical Modeling in Mathematics Education","authors":"H. Pollak, S. Garfunkel","doi":"10.7916/JMETC.V0I0.658","DOIUrl":"https://doi.org/10.7916/JMETC.V0I0.658","url":null,"abstract":"Mathematical Modeling is being introduced as a new product into the complex system of Mathematics Education. It has to fit with the existing parts and interfaces in this system. As one example, we will consider the effect of mathematical modeling on the transition from secondary to tertiary education. If mathematical modeling is of greater importance to the planners at one of these two levels of education than at the other, then stresses may result. As a second example, we propose to examine changes in teacher education necessitated by the introduction of mathematical modeling at the secondary level. Ideally, one might wish to prepare teachers to teach mathematical modeling by concentrating purely on modeling without the distraction of new mathematical ideas, but it is not clear that this can always be done. Finally, we plan to make some comments on the effect of mathematical modeling has on the relationship between mathematics education and mathematics itself. Each of these should gain from cooperation with the other.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article describes the evolution of an analytical scheme that describes the dimensions of powerful mathematics classrooms—classrooms that produce students who are powerful mathematical thinkers. Such classrooms engage students with coherent and connected mathematics; they provide all students opportunities to do mathematical thinking. They help students develop a sense of mathematical agency and authority, and they employ formative assessment, finding out what students understand and building on those understandings. I discuss how this scheme can be used as the basis for professional development, and how a school district might take up a full-fledged professional development agenda.
{"title":"What Counts in Mathematics (and Other) Classrooms? A Framework for Looking at What Matters, and Thoughts About How One Might Use These Ideas for Professional Development","authors":"A. Schoenfeld","doi":"10.7916/JMETC.V0I0.663","DOIUrl":"https://doi.org/10.7916/JMETC.V0I0.663","url":null,"abstract":"This article describes the evolution of an analytical scheme that describes the dimensions of powerful mathematics classrooms—classrooms that produce students who are powerful mathematical thinkers. Such classrooms engage students with coherent and connected mathematics; they provide all students opportunities to do mathematical thinking. They help students develop a sense of mathematical agency and authority, and they employ formative assessment, finding out what students understand and building on those understandings. I discuss how this scheme can be used as the basis for professional development, and how a school district might take up a full-fledged professional development agenda.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71368922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the horizontal bar that is often referred to as “minus sign,” the authors introduce a novel notation intended to address this ambiguity. In this system, the symbol “−” is reserved exclusively for subtraction. The four arithmetic operations and the concept of a number's opposite are then illustrated in light of such a notational shift. A valuable aspect of this excursion is that it encourages teachers to reflect on the relationship between some important mathematics and the pedagogical approaches they now use.
{"title":"Toward A Coherent Treatment of Negative Numbers","authors":"K. Kreith, Al Mendle","doi":"10.7916/JMETC.V4I1.775","DOIUrl":"https://doi.org/10.7916/JMETC.V4I1.775","url":null,"abstract":"The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the horizontal bar that is often referred to as “minus sign,” the authors introduce a novel notation intended to address this ambiguity. In this system, the symbol “−” is reserved exclusively for subtraction. The four arithmetic operations and the concept of a number's opposite are then illustrated in light of such a notational shift. A valuable aspect of this excursion is that it encourages teachers to reflect on the relationship between some important mathematics and the pedagogical approaches they now use.","PeriodicalId":30179,"journal":{"name":"Journal of Mathematics Education at Teachers College","volume":"4 1","pages":"52-54"},"PeriodicalIF":0.0,"publicationDate":"2013-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71369114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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