Mathematics Concepts and Skills for Elementary School Teachers
- Page ID
- 157542
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 1: Mathematical Thinking, Problem Solving and Math as a Language
- This page emphasizes the significance of mathematical thinking and problem-solving in elementary education, suggesting that these skills enhance understanding and foster positive attitudes toward math. It highlights the importance of early exposure to problem-solving for future achievement and encourages teachers to create engaging, collaborative environments.
- 2: Sets, Counting, and Numeration- Connecting Early Math to Advanced Ideas
- This page emphasizes the significance of set theory in elementary education for foundational mathematics and daily applications. It discusses how set theory enhances children's problem-solving and logical reasoning. Future teachers need a solid understanding of set concepts to guide students effectively. The chapter includes learning objectives focusing on various number systems and set manipulation skills, ultimately linking mathematical patterns to real-world scenarios.
- 3: Building Number Sense- Understanding Whole Number Operations and Their Properties
- This page emphasizes the significance of whole number operations (addition, subtraction, multiplication, division) in everyday life and education. It outlines learning objectives for future elementary teachers, focusing on fostering number sense in students. Key concepts include operation properties, mental computation strategies, and the application of mathematical models.
- 4: Strengthening Number Sense - Strategies, Algorithms, and Estimation
- This page highlights the need for teaching whole-number computation with a focus on understanding rather than memorization. It advocates for developing number sense and problem-solving skills in students through mental math and diverse strategies. The text promotes an environment that values multiple approaches and a growth mindset, equipping learners for real-life applications. A narrative featuring a character named Morgan showcases practical uses of mathematics, reinforcing these concepts.
- 5: The Foundations of Number Theory
- This page discusses the foundational role of number theory in elementary mathematics, emphasizing its importance for prospective teachers in developing a flexible number sense and fostering students' confidence. Key learning objectives include analyzing number properties, identifying prime numbers, and computing GCF and LCM.
- 6: The Story of Fractions
- This page explores the historical significance and practical uses of fractions, originating around 1600 B.C.E. in ancient Egypt. It highlights the real-life needs that led to the development of fractions and their importance in advanced mathematics. Learning objectives include modeling and applying fractions in everyday situations, exemplified through a narrative about Morgan and her grandfather making tamales, showcasing the relevance of fractions beyond academic contexts.
- 7: From Parts to Percents- Decimals, Ratios, Proportions, Percentages
- This page emphasizes the importance of a strong foundation in fractions for students' understanding of decimals, percentages, ratios, and proportions. In upper elementary grades, the focus is on conceptual understanding and real-world applications. By Grade 7, students should analyze and convert these concepts, solve ratio problems, and use scientific notation, highlighted by relatable stories like Morgan and Grandpa at a baseball game.
- 8: Integers
- This page emphasizes the need for future elementary teachers to understand students' difficulties with integer operations due to the complexity of negative numbers. It advocates for teaching strategies such as manipulatives and real-world analogies to enhance comprehension. The text details learning objectives and critical questions, underlining the role of integers in problem-solving and algebraic reasoning.