CURRICULUM TOPIC STUDYSearch Mathematics Supplements
Find your supplement in 3 simple steps!Search Results For Mathematics Supplements
A video instructional series on statistics. 26 half hour video programs are available with an emphasis on doing statistics. The series is designed and organized around the NCTM content standards. The video clips and supporting resources are developed for elementary and middle school teachers looking to enhance their own understanding of statistical concepts. A great resource to use in conjunction with the readings from section I.
CTS Topic(s):
? Bar Graphs, Histograms and Line Graphs (session 1, 2, 3)
? Line Plots, Stem and Leaf Plots, Box Plots and Histograms (session 3, 5)
? Measures of Center and Spread (session 2,3,4,5)
? Probability (session 6,7,8, 9)
? Sampling (session 1, 6, 8, 9)
? Scatter Plots and Correlation (session 3,4,5, 7)
? Statistical Reasoning (session 1-9)
? Summarizing Data (session 1-9)
A short video clip (4 minutes) reflecting estimation and computation skills in a fourth grade classroom setting. Students are shown solving math problems, using multiplication of whole numbers, as a group. Estimation strategies, problem solving and communication skills are stressed. This short video clip could be used to supplement section II.
A series of video clips (? hour each) with accompanying support materials such as problem solving activities, online and print resources, interactive activities and demonstrations which help increase teachersí expertise and content knowledge as it relates to number and operations. The online series is a useful resource to supplement section I.
CTS Topic(s):
? Estimation (sessions 1-9)
? Proportionality (session 8)
This book discusses many mathematical topics providing key concepts, connections, teaching tips and learning pitfalls. Corresponding NAEP and/or TIMSS are also given. This book would be an additional resource to sections II, III and IV.
Video instructional series consisting of 26 programs designed to be used by students or as a review of content matter for teachers. Illustrations and examples are used to solve real-world problems. This series could be used to supplement the readings from section I.
This article describes a variety of computational techniques for addition, subtraction, multiplication and division of whole numbers. This resource could be used in conjunction with sections I, II and III.
This article illustrates the misconceptions that students have when using the equals sign and describes an activity used with students to develop the foundation for an accurate conception of equivalency. The author states that developing an accurate understanding of the equal sign is the basis for comprehending equations and inequalities. This article could be used to supplement the readings from sections II and IV.
The research summarized in this Volume of In Brief focuses on the ability of elementary students to reason algebraically. The articles can be used with CTS Section IV.
Description: A summary of the structures used by students for adding and subtracting mulitdigit numbers. The article identifies and describes categories of methods devised by students to sovle the problems as well as typical errors that may arise with each method. This article can be used to supplement sections II and IV.
This article reports research findings regarding the learning and teaching of proportional reasoning from the Rational Number Project. Examples of different types of tasks that assess proportionality along with solution strategies are included. This would be a great supplement to the readings from section IV.
This article describes developing fluency with addition and subtraction of fractions by focusing instruction on the big idea of operating with like-size units. A sequence progression of addition and subtraction problems as well as some samples of student work is illustrated. This resource could be using to supplement section II.
12. Correlation
This video can be used with CTS Section I to develop teacher content understanding. The video uses an every day application of the relationship between a baseball player's salary and home run statistics to help teachers understand the concept of correlation.
This section in Curriculum and evaluation standards for school mathematics focuses on evaluation of standard 7 ñ Reasoning and can be used as a supplement to Section II and IV. The focus of this section is on considering the implications for assessing student reasoning which often cannot be seen effectively within verbal or written responses. Examples of tasks are included that demonstrate assessment techniques that address different types of reasoning.
An article that looks at studentsí responses to open-ended questions related to sampling. The objective of the analysis is to understand the characteristics of studentsí constructions of the concept of sample. Responses are characterized in relation to the content, structure and objectives of statistical literacy. Six categories of construction are identified and described with intent of developing an understanding of representation and to plan appropriate interventions. This resource would be helpful in illuminating readings from sections II, III and IV.
Can be used with Section II to examine implications for instruction and Section IV for research on student learning
This article describes the implementation of an activity designed to confront a common misconception about variable. The article describes common misconceptions held by middle level students and describes a problem situation designed to uncover studentsí misconceptions. This article could be used to supplement the readings from sections II and IV.
This resource helps readers make sense of mathematics interweaving content ideas with instructional implications. Sixteen chapters reflect the view that mathematics can be taught through a problem-solving approach that motivates children and builds their confidence as they learn. Chapter 9 (pages 120-137) supplements Section II by providing instructional implications for number development in the early grades.
This article discusses teacherís own subject-matter knowledge of division of fractions as well as the likely sources of common misconceptions held by children. The reading can be used to supplement sections I, II and IV.
This article discusses teacherís own subject-matter knowledge of division of fractions as well as the likely sources of common misconceptions held by children. The reading can be used to supplement sections I, II and IV.
A brief overview of the importance of measurement in science and daily life. Standards from NSES and NCTM are summarized as well as student difficulties and misconceptions with various measurement topics. Additional resources, books, web links and references are included. This brief article can be used to supplement the readings from section IV.
This article explores misconceptions that students hold about sampling techniques on surveys and discusses implications for instruction. This brief article would supplement the reading from section IV.
The authors propose ìintuitive rulesî that students use to reason about mathematics and science concepts. The book provides many examples how these rules can be used to interpret the misconceptions many students have about mathematical concepts. This resource book can be used to supplement the readings from section IV.
How Students learn uses the principles and findings from How People Learn within the context of the mathematics classroom. An introduction to the principles as they apply to mathematics is included in chapter 2, whole numbers at the elementary level is the focus of chapter 3, rational numbers at the middle level is the focus of chapter 4 and chapter 5 focuses on functions at the high school level. This would be an additional reference to sections II, III and IV.
This article describes surprising misconceptions revealed by a fifth-grade student during a series of interviews about probability. A brief, but informative article that would supplement the readings from section IV.
25. Making Sense of Graphs: Critical Factors Influencing Comprehension and Instructional Implications
This article outlines critical factors that appear to influence graph comprehension and identifies instructional implications. The factors identified are purpose, task characteristics, discipline characteristics and reader characteristics. A sequence for ordering the introduction of graphs is proposed and ways instruction may be modified to promote graph sense making. This article would be a good addition to sections II and IV.
This article describes the results of a multi-year research project on algebraic reasoning in middle school students. The article describes middle school studentsí understandings and/or misunderstandings of two core algebraic ideas ñ equivalence and variables. The article gives student response examples and discusses implications for instruction. This article could be used to supplement the readings from sections II and IV.
Description: A series of video clips (? hour each) with accompanying support materials such as problem solving activities, online and print resources, interactive activities and demonstrations which help increase teachersí expertise and content knowledge as it relates to number and operations. The online series is a useful resource to supplement section I.
? Numbers and Number Systems (session 1, 2)
? Place Value (session 3)
? Computation and Operations (session 4)
? Factors and Multiples (session 5 and 6)
? Fractions (session 7)
? Decimals (session 7)
? Rational Numbers (session 8)
? Ratio and Proportion (session 8 and 9)
? Percent (session 9)
A collection of essays which offer insights into the emphasis on statistics in the K-12 mathematics curriculum. Through the investigation of several projects, the authors explore the enhancement and assessment of student learning in the areas of collection, presentation and interpretation of data. The essays cover content, teaching, learning and assessment. The statistics content, the extent of coverage recommended for various grade levels as well as student understandings are highlighted. This resource could be used in conjunction with the readings from section I and II.
Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Sections can be used as supplements for Section IV.
This article describes a study conducted with 200 high school students to learn about studentís preconceptions about probability. Students develop concepts of probability without formal study of the concepts. The article summarizes the findings and includes the survey that was used with secondary students. This article would supplement the reading from section IV.
The selected reading, pages 313-315, can be used for addtional readings in Section IV to examine research on student learning.
This is an online resource that provides teachers with a rationale for the content topics, activities with supporting background, additional connections to the standards, other related resources as well as connections across grade spans. A good resource to supplement the readings from sections I, II and III.
This article defines statistical literacy as well as outlining important components of a statistics course. Section 3.2 specifically refers to several misconceptions highlighting student understandings or misunderstandings. This would be a good supplement to section I and IV particularly at the high school level.
This book illustrates the development of studentsí understanding of statistical concepts. The author gives many examples that highlight how students think about important statistical concepts and supports findings based on research. Student thinking is explained in relation to a variety of tasks based on sampling, graphical representations, averages and chance. This resource could be used to supplement the readings from section I, II, III and IV.
This article is a brief overview of the results of a research project focusing on solution strategies algebra students used to solve non-linear function problems. The article focuses on the variety of strategies, the relationship to achievement and using multiple representations. Examples of the constructed response items and student solutions are given. This reading could be used to supplement readings from section II and IV.
This paper summarizes a research study conducted on first year college level students taking an introductory statistics course. There are many interesting and applicable findings for high school statistics. The article focuses on studentsí thinking on variability, what students can do and transitions in their understandings. Many examples are given including, box plots, histograms, sample, center and spread. These finding could supplement sections II and IV.
Chapter 3 of this resource can be used to supplement Section IV: Research on Student Learning for topics in the Numbers and Operations Category. The Chapter includes information about 1) Student difficulties, confusion, and misconceptions and 2) Factors contributing to students' difficulties, confusion, and misconceptions.
This article can be used to supplement CTS Sections III and IV. The article describes the design and the results of an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop in pupils a disposition toward (more) realistic mathematical modeling. This goal is achieved by immersing them in a classroom culture in which word problems are conceived as exercises in mathematical modeling, with a focus on the assumptions and the appropriateness of the model underlying any proposed solution.
This article supplements Section IV by providing information about the need to consider social interaction within the mathematics classroom. Researchers have identified that ìstudentsí apparently bizarre mathematical behaviorsî frequently cannot be accounted for solely in terms of conceptual limitations. This article suggests moving past the ëpurely cognitiveí to the role played by social issues for students.
This article summarizes the intuitively based misconceptions that many students have in regards to probability concepts. The findings highlight that many misconceptions grow stronger with age, while others grow weaker. This article would supplement the reading from section IV.
Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents. Each volume highlights strategies, models and big ideas through classroom examples, samples of student work, anecdotes and illustrations. Each volume can be used to further illustrate readings from section II, III and IV.
Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents. Each volume highlights strategies, models and big ideas through classroom examples, samples of student work, anecdotes and illustrations. Each volume can be used to further illustrate readings from section II, III and IV.
Each book in this series of three illuminates the progression of strategies, the development of big ideas and the mathematical models that children construct. The first volume focuses on how young children develop an understanding of number, addition and subtraction. The second volume focuses on how students develop an understanding of multiplication and division. The third volume highlights how students develop an understanding of fractions, decimals and percents. Each volume highlights strategies, models and big ideas through classroom examples, samples of student work, anecdotes and illustrations. Each volume can be used to further illustrate readings from section II, III and IV.
This article describes a technology-based approach for dealing with a misconception that some students hold concerning the equivalency of geometric transformations. The article looks at students studying transformations as mathematical entities and not just as procedures to apply to shapes. Students use technology-based activities to help rectify commonly held misconceptions. This resource would be a good supplement for sections II and IV.
The video clips in this example illustrate the range in understanding of numbers and their relationships of students in grades Pre K-2. The clips display students demonstrating different levels of understanding numbers and place value concepts. These clips can be used with section II
This article provides information about the scope and nature of studentsí difficulties with modeling and solving non-routine word problems using addition or subtraction. Highlighted misconceptions about numbers and arithmetic operations can be used to supplement section IV.
This article provides information about the scope and nature of studentsí difficulties with modeling and solving non-routine word problems using addition or subtraction. Highlighted misconceptions about numbers and arithmetic operations can be used to supplement section IV.
This article examines four areas of difficulty students have with graphing and modeling. The four areas are identified as connecting graphs with physical concepts, connecting graphs with the real world, transitioning between graphs and physical events, and building graphical concepts through student discourse. The article looks at studentsí misconceptions and the role of technology in helping to form accurate graphical concepts. This article could be used in conjunction with the readings from section IV.
This article examines four areas of difficulty students have with graphing and modeling. The four areas are identified as connecting graphs with physical concepts, connecting graphs with the real world, transitioning between graphs and physical events, and building graphical concepts through student discourse. The article looks at studentsí misconceptions and the role of technology in helping to form accurate graphical concepts. This article could be used in conjunction with the readings from section IV.
This article discusses the role of studentís everyday knowledge of decimals in supporting the development of their knowledge of decimals. Students using contextual problems with decimals are able to build on their understanding of decimals. The problems used tap common misconceptions about decimal fractions so could be used to supplement section IV.
This article describes how students generalize and formalize patterns using student developed schemas including ìsubtracting outî and ìbuilding upî. The article includes samples of student work including studentsí explanations for each schema. This article could supplement readings from section II and IV.
