Annotated Bibliography Numeracy – Building a Community of Practice K – 12 The following is a brief listing of possible articles that may continue a discussion around numeracy with your team. It is by no means exhaustive and serves as a starting point to spur thought and reflection. In the spirit of reflection, it is expected that teams will add to this list and share with others as we continue to collectively move forward with this learning. ARTICLES Pr. Jr. Int . Sr. K- 12 Gen eral Dan ce Art Mus ic Scien ce Phys. Ed. Socia l Studi es Cross - curri cular Ali, R. (2010). Effect of using problem solving method in teaching mathematics on the achievement of mathematics students. Asian Social Science 6 (2), 67-72. The purpose of this quantitative study is to investigate the effects of using the problem solving method on grade eight students in public and private elementary schools in Pakistan. There was a significant difference between teaching concepts in the traditional method versus the problem solving method. The author presented referenced literature to support his purpose. The conclusions were based on student scores on mathematics achievement tests. Knowledge, comprehension and application were areas assessed for the purpose of this study. There were recommendations offered by the author based on his findings and these included changing the focus of textbooks to problem based learning, using problem based learning in the classroom to improve student achievement and to prepare teachers to include problem based learning into their practices. Arcavi, A. (2002). Chapter 2: The everyday and the academic in mathematics. Journal for Research in Mathematics Education. Monograph, 11, Everyday and Academic Mathematics in the Classroom, 12-29.
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Annotated BibliographyNumeracy – Building a Community of Practice K – 12
The following is a brief listing of possible articles that may continue a discussion around numeracy with your team. It is by no means exhaustive and serves as a starting point to spur thought and reflection. In the spirit of reflection, it is expected that teams will add to this list and share with others as we continue to collectively move forward with this learning.
ARTICLES Pr. Jr. Int. Sr. K-12 Genera
l
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Social Studies
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arAli, R. (2010). Effect of using problem solving method in teaching
mathematics on the achievement of mathematics students. Asian Social Science 6 (2), 67-72.
The purpose of this quantitative study is to investigate the effects of using the problem solving method on grade eight students in public and private elementary schools in Pakistan. There was a significant difference between teaching concepts in the traditional method versus the problem solving method. The author presented referenced literature to support his purpose. The conclusions were based on student scores on mathematics achievement tests. Knowledge, comprehension and application were areas assessed for the purpose of this study. There were recommendations offered by the author based on his findings and these included changing the focus of textbooks to problem based learning, using problem based learning in the classroom to improve student achievement and to prepare teachers to include problem based learning into their practices.Arcavi, A. (2002). Chapter 2: The everyday and the academic in
mathematics. Journal for Research in Mathematics Education. Monograph, 11, Everyday and Academic Mathematics in the Classroom, 12-29.
The author examines “everydayness, “mathematization” and “context familiarity” in connecting/integrating mathematics between the classroom and the “outside world”. These three concepts are explored in more detail in the body of the article. Examples of each of the three concepts are drawn from the author’s work with pre-service teachers, curriculum development and research literature. Abraham Arcavi does include “Academic Everydayness” as part of the “everydayness” in teaching mathematics by illustrating two graphical solutions to an equation as provided by teachers. The author proposes the need for considering different practices and approaches in delivering the curriculum especially in the area of “Academic Everydayness”. Accompanied by examples, the theme of students finding different solutions to a mathematical problem are
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arfurther explored in the “mathematization” and “context familiarity”.Attard, C., & Northcote, M. (2011). Mathematics on the move: using
mobile technologies to support student learning (part 1). Australian Primary Mathematics Classroom. 16 (4), 29-31.
This is an article focusing on the use of iPod Touch and iPad in the primary mathematics classroom. The authors emphasize the importance of pedagogy driving technology and not in the reverse case. Rocket Math, Geometry Test, Maths Addicted, Basic Math and MathBoard Addition were apps that the authors deemed appropriate for increasing number operations. The following five apps: Red Dragonfly Mathematics Challenge, Kenken: Train Your Brain Lite, LetsTrans Lite, Dice Puzzle and Sukoku are briefly described and commented on their potential pedagogical value for problem solving in the classroom. 2011 World Fact Book, iBluepring, iBrainstorm, Keynote and Show Me were potential tools for the students to use as apps where pedagogy drive technology. This article provides teachers a snapshot into selecting tools for a problem solving mathematics classroom.Attard, C., & Northcote, M. (2012). Mathematics on the move: using
mobile technologies to support student learning (part 2). Australian Primary Mathematics Classroom. 17 (1), 29-32.
Global positioning system (GPS) and other hand-held devices’ uses in the primary classroom are the focus of this article. Position of individual, distance travelled, time travelled, speed and estimated time remaining to destination are some information provided by the GPS. Together with this information students could use the GPS like a pedometer and make appropriate calculations. Webcams on the internet are also mentioned to provide potential mathematical exercises for teachers. A hand-held infra-red thermometer could be used for measuring temperature and then connected to a laptop for subsequent mathematical tasks. The authors introduce the readers to tools that could be used indoors or outdoors and complement computational strategies in the mathematics classroom.Benzanson, C, & Killion, J. (2001). Moving math outdoors. Green Teacher
64 (Spring), 31-33.
The question “When am I every going to use this?” leads the article. The backdrop is the schoolyard. The authors provide a case for engaging students in mathematics outside of the classroom. Example primary grade activities cover the following concepts: patterns, number
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arsense, geometry, measurement and graphing. Example intermediate and middle grade activities cover the following concepts: collecting and describing data, number operations, geometry, measurement and estimation. A detailed lesson on the topic of sampling a plot of land is included in the text. The authors provide a starting point for teachers to make use of their respective schoolyard.Bruno, J. (2011). Math movement: The integration of geometry and dance.
Hofstra University). ProQuest Dissertations and Theses, Retrieved from http://search.proquest.com/docview/877593961?accountid=14771
This Master of Arts in Elementary Education dissertation investigates the improvement of skills levels in dance and mathematics. The participants in the study are grades three and four students. The dance classes were held in a neighbourhood dance studio. Geometric concepts and spatial thinking are infused in the study. There are pre and post comparisons concluding with benefits in skills development in math and dance. Seventeen detailed lesson plans are included in the appendix as well as a rubric to assess learning goals.Busadee, N., Laosinchai, P., & Panijpan, B. (2012). Finding possibility and
probability lessons in sports. The Mathematics Teacher 105 (5), 372-378.
The application of sports into the teaching of probability is the focus of this article. The concepts of permutations and combinations were taught using table tennis, soccer (x2), track relay, football and golf. A description of each problem is given to the reader accompanied by the solution. An extension problem with golf is included in the article. The lesson was over a five one-hour time period. The authors tested the sequence of the lesson twice and used a control group to find improvements in test scores.Civil, M. (2002). Chapter 4: Everyday mathematics, mathematicians’
mathematics, and school mathematics: Can we bring them together? Journal for Research in Mathematics Education. Monograph, 11, Everyday and Academic Mathematics in the Classroom, 40-62.
The article explores the union between a mathematician’s math and mathematics for children outside of the classroom through an exploratory study involving a fifth-grade class. The author recognizes the
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arimportance of the mathematics in the classroom but acknowledges that there is also a need to integrate and provide activities that connect mathematics from student experiences outside of the classroom. Answering the question: “(At least) three kinds of mathematics?” the author provides a brief literature survey and characteristics on “School Mathematics”, “Mathematicians’ Mathematics in the School Context” and “Everyday Mathematics”. The teacher and the author developed a thematic module involving games with an attempt to address students’ experiences outside the classroom on the topic of geometric patterns. The next part of the student involved the teacher introducing the concept of geometry which included examining patterns and incorporating related activities in Native American art. Tessellations were the final area of study for the class. The study found that there was greater student participation in “everyday” mathematics but an increase when there were mathematical discussions with peers in the academic matters part of the module.Edelson, R. J., & Johnson, G. (2004). Music makes math meaningful.
Childhood Education 80 (2), 65-70.
The article focuses on the interdisciplinary nature found between music and mathematics. The authors endorse the integration of music and mathematics. Activities through song and musical instruments are used to connect pupils with mathematical concepts involving patterns, serial order, graphing, sorting, classification and Venn diagrams. The concept of fractions is incorporated by creating a musical arrangement with partial notes is one example of a cross-curricular activity for the students. The integrated activities provide examples of addressing the kinesthetic and auditory types of learning. The strategies implemented and the selections of musical instruments allow the students to represent and communicate their understanding of mathematical concepts. The examples are descriptive in nature and are not presented in a step by step lesson plan format. However, the article offers a starting point for teachers to actively engage and connect students with music as they learn mathematics.Edens, K., & Potter, E. (2007). The relationship of drawing and
mathematical problem solving: Draw for math tasks. Studies in Art Education 48 (3), 282-298.
This academic study examines children’s drawings with their spatial understanding and problem solving in mathematics. Findings show “…that level of spatial understanding and use of schematic drawings both were significantly correlated to problem solving performance” (p. 282). The
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arstudy is supported by research. There are samples of children’s drawings in the article. Teaching strategies are included by the authors. An extensive reference list accompanies this article for an expanded search for related literature.Edwards, A., & Ruthven, K. (2003). Young people’s perceptions of the
mathematics involved in everyday activities. Educational Research 45 (3), 249-260.
This is an exploratory study involving grade seven and ten students’ perceptions of mathematics in five “everyday” activities- Dressmaking/Making trousers, playing snooker/pool, knitting a cardigan, making a Lego robot and playing chess. The data was based on interviews with the participants. The study did find that the students were able to identify mathematics more in the dressmaking/making trousers activity than the others. However, there were mathematical concepts identified for each activity with measurement and angles being the most frequently mentioned by the students. The study provides a reflective educator to consider the importance of selecting tools and strategies that integrate mathematics and “everyday” mathematics.Gainsburg, J. (2008). Real-world connections in secondary mathematics
teaching. Journal of Mathematics Teacher Education 11 (3), 199-219.
Gainsburg, identifies the initiatives and a range of practices with “real-world” connections and mathematics teaching. There is a comprehensive list of literature connected to this topic. Sixty-two secondary school mathematics teachers were surveyed regarding their understanding and use of “real-world” connection in their classrooms. Five teachers were chosen for further investigation concerning their respective practice. The teachers were asked for written descriptions in the following categories: Format- The teaching mode in which the connection was made; Feature- Any special aspect enhancing the authenticity of the connection; Context- The real-world setting or object to which the mathematics was connected; and Mathematics- The mathematical concept or skill involved. The study did show that a proper design and integration of “real-world” connections provides “…a strong foundation for learning mathematical ideas.”Harrell, G. K. (2008). Integrating mathematics and social issues.
Mathematics Teaching in the Middle School 13 (5), 270-276.
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arHarrell looks to local issues that would connect with the math
curricula. The main subject in this article is the construction of new roads. The author provides descriptive examples of the mathematics that would be involved such as calculating the necessary acreage to build a road. Sample calculations are included in the text. The students would also be asked to role play civic officials in the debate of whether a road should be built or finding an alternative route. The middle school mathematics teacher will find this material to be jumping off point for potential ideas connecting social studies and mathematics.Heavey, J. M. (1998). The effects of integrating literature and mathematics.
Fairleigh Dickinson University). ProQuest Dissertations and Theses, 35 p. Retrieved from http://search.proquest.com/docview/304470763?accountid=14771
This Master of Arts in Teaching dissertation examines the integration of literature and mathematics through a study of grade one pupils on the topic of measurement using books with mathematical concepts. The author writes: “The perception of math changed as its relevancy and practical applications became apparent. The learning atmosphere was charged with enthusiasm and participation because the students understood the reason why they were seeking a solution.” A “Recommended Books for Teaching Math” was included in the Appendix as well as a lesson plan and a worksheet. The paper provides supporting research for integrating literature and mathematics. In conjunction with the application of literature, the author also promotes the appropriate classroom environment for making connections.House, P. A. & Coxford, A. E. (Eds.). (1995). Connecting Mathematics across
the Curriculum. Reston, Virginia: National Council of Mathematics of Teacher of Mathematics.
Though the yearbook was published in 1995, the cross-curricular theme of mathematics is applicable today. This reference is intended for K-12 teachers. The book is divided into five parts: “General Issues”, “Connections within Mathematics”, “Connections across the Elementary School Curriculum”, Connections across the Middle School Curriculum”, and “Connections across the High School Curriculum”. The articles provide suggestions for activities with accompanying descriptions in text and in some cases with graphics. References are provided at the end of each article. In total there are 26 articles.
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arMoschkovich, J. N. (2002). Chapter 1: An introduction to examining
everyday and academic mathematical practices. Journal for Research in Mathematics Education. Monograph, 11, Everyday and Academic Mathematics in the Classroom, 1-11.
The two purposes served for writing the articles were to address the juxtaposition of academic mathematical practices and everyday mathematics in the mathematics classroom. The author expands the discussion by including school mathematics and workplace mathematics into the vernacular. Moschkovic presents two proposals: problems and activities from workplaces and students’ experiences outside of the school; and “making generalizations across applied problem situations.” The author then proceeds to provide literature references connected to each proposal. In the end, Moschkovic states, “…classroom teachers can connect students’ practices to the practices of mathematicians…teachers can connect mathematicians’ practices to students’ classroom activities by encouraging them to find or pose problems about mathematical objects, make generalizations across situations, and construct mathematical arguments.”Northcote, M. (2011). Step back and hand over the cameras! Using digital
cameras to facilitate mathematics learning with young children in k-2 classrooms. Australian Primary Mathematics Classroom. 16 (3), 29-32.
Northcote provides an argument for the use of digital cameras as tools in teaching mathematical concepts in the primary classroom. There are cited references included in the case for using the digital camera. Examples are included for the reader to use in the classroom: graphing by using photos of shoes; space and geometry concerning symmetry, parallel, vertical and horizontal lines; a math photo journal where student write reflections or interpretations of their photos in the context of math concepts such as shapes, counting, positions etc. Activating prior knowledge for the student is also covered in the article. The author provides the reader with a starting point for the potential uses of the camera in the classroom. “Real world” mathematics certainly connects with classroom mathematics in this article.Piatek-Jimenez, K., Marcinek, T., Phelps, C. M., & Dias, A. (2012). Helping
students become quantitatively literate. The Mathematics Teacher 105 (9), 692-696.
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arThe authors define the meaning of quantitative literacy (QL);
question whether it should be incorporated into the traditional classroom; how it differs from the traditional mathematics course and provides sources of quantitative learning problems that could be used in middle school, high school and college curricula. Content, context, teaching methodology and assessment are elaborated on in the explanation to differentiate QL from the traditional way of teaching mathematics. The authors advocate the inclusion of “Real-world” mathematics in promoting quantitative literacy. Examples of sources such as newspapers, student journal entries, and problems supporting QL are included in the article.Rose, T. D., & Schuncke, G. M. (1997). The link between social studies and
mathematics. The Clearing House 70 (3), 137-140.
The authors note the traditional pairings of subjects i.e., math and science, and language arts social studies. They propose an interdisciplinary union between social science and mathematics in the middle school years. Problem solving is the focus between the two disciplines. Problem solving in mathematics is referred to in cited literature. Problem solving in social studies is clearly identified as two processes: Exploration and Inquiry. Each of these two processes is presented in a step-by-step format with the Inquiry portion being more descriptive. A subsequent table shows the two processes in problem solving as compared to each other and to the mathematics approach. In the end, the teacher has the opportunity for the students to reflect and connecting when approaching a problem in the social studies and mathematical contexts.Sakshaug, L. E., & Wohlhuter, K. A. (2010). Journey toward teaching
mathematics through problem solving. School Science and Mathematics 110, (8), 397-409.
A group of teachers are learning to teach through problem solving in a “Teaching Elementary School Mathematics” graduate course. The course enabled 41 participant teachers to feel more comfortable in teaching mathematics realizing the importance of group work while problem solving. The study involved the teaching of mathematics that differed from the teachers’ experiences in how they were taught mathematics. The teacher participants tested their abilities to be problem solvers as well as action researchers. Data collected involved reflections by the teachers’ success and challenges concerning their own ability to choose and solve problems and the implementation of the methodology with students in the classroom. The study showed the importance of group work
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arin student engagement and success in mathematical problem solving.Schettino, C. (2011/2012). Teaching geometry through problem-based
learning. The Mathematics Teacher 105 (5), 346-351.
Schettino proposed to explore a problem-based learning model for the geometry unit upon reflection and examination of his current text- based unit. Reference literature on problem-solving curriculum is included in the article. The author gives his own interpretation of problem-based learning: “An instructional approach of curriculum and pedagogy where student learning and content material are constructed (and co-constructed) through the use, facilitation, and experience of contextual problems in a decompartmentalized, threaded topic format ins a discussion-based classroom setting where student voice, experience, and prior knowledge are valued.” The purposeful approach by the author is evident in the article as he articulates the reasons for the specific activities and the anecdotal data resulting from implementation with the students. The author does state the necessary balance between a teacher’s “…attempt to balance respectful intervention with presentation of new material and elicitation of information from the students.”Shatzer, J. (2008). Picture book power: Connecting children’s literature
and mathematics. The Reading Teacher 61(8), 649-654.
Shatzer offers the elementary school teacher a starting point for integrating literature and mathematics. The author explores and connects math concepts into two categories with respective to literature: “Children’s Literature With Specific Math Content” and “Children’s Literature Without Specific Math Content”. Eating Fractions and A Chair for My Mother are two picture books found in their respective tables showing the math concept and possible employable strategies for teachers. Shatzer offers ideas and strategies for each category. Teachers who find it a challenge to include stories without specific math content will find a very good starting point in this article in their unit planning. The article is supported by reference on the mathematical processes. Literature cited is also included as a separate section. The ideas and strategies offered are in response to the interdisciplinary methodologies involving English language arts and mathematics.Stylianides, G. (2010). Engaging secondary students in reasoning and
proving. Mathematics Teaching 219, 39-44.
The author outlines the components required for students
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aracquiring reasoning and proving capabilities. The article is aimed at secondary school teachers. A table “An analytic framework of reasoning-and-proving” is included in the article with the following guiding question: “What are the major activities involved in reasoning-and-proving?” The two column headings are “Making generalizations” and “Developing arguments” with accompanying rows: “Mathematical component”, “Learner component” and “Pedagogical component”. Examples accompanied by explanations were given for each component. The model serves as a guide for teachers seeking direction for forming questions for students, showing a “relationship between proof and other activities.”Westwood, P. (2008). What Teachers Need To Know About Numeracy.
Victoria, Australia: ACER Press.
This chapter book presents a comprehensive look at numeracy for the pre-school, elementary and secondary school teachers. There is a list of identified thematic issues at the beginning of each chapter. The thematic issues are thoroughly expanded and supported by researched information. There is an extensive and valuable reference section at the back of the book. This reference book belongs in a teacher’s professional library.Wilcox, B., & Monroe, E. E. (2011). Integrating writing and mathematics.
The Reading Teacher 64 (7), 521-529.
There are four “Pause and Ponder Questions that the authors attempt to address in this article: “Why might we want to integrate writing and mathematics? How can mathematics serve as a context for developing the writing process? Why use writing as a tool for developing mathematical thinking? How can teachers integrate writing, with or without revision, and mathematics? The authors present six ideas for integrating writing with mathematics at the elementary level: Writing Without Revision- Learning Logs, Think-Write-Share, Note-Taking/Note-Making and Writing With Revision- Shared Writing, Class Book, Alphabet Books. A student example of each particular topic accompanies each idea: “Definitions and Examples of Mean, Median, and Mode” and “…Probability”, “Example Showing a Clear Understanding of Equivalent Fractions” and “Example of Equivalent Fractions, Before and After Revision”, “Note-Taking/Note-Making: A Fifth Grader’s Conception of Integers”, “A Shared Writing About Geometry Composed and Revised by Third Graders and Their Teacher”, “A Class Book Page About Word Problems Written and Illustrated by Fourth Graders”, and “An Alphabet
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arBook Page: ‘T Is for Transformation’ Completed by a Fifth Grader”, respectively. The authors provide purpose, description and some teacher and student experiences/reflections for each particular idea.
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