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Algebraic Thinking

Algebraic Thinking. By: Nicole Davis Amanda Rippley Amanda Rhoads. What is Algebraic Thinking?. Possible definitions: “The ability to think logically about unknown quantities and the relationships between them(Molly Argo).”

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Algebraic Thinking

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  1. Algebraic Thinking • By: • Nicole Davis • Amanda Rippley • Amanda Rhoads

  2. What is Algebraic Thinking? Possible definitions: • “The ability to think logically about unknown quantities and the relationships between them(Molly Argo).” • “One’s ability to generate, represent, and justify generalizations about fundamental properties of algebra(Molly Argo).” • "algebraic thinking" has become a catch-all phrase for the mathematics teaching and learning that will prepare students for successful experiences in algebra and beyond. (Shelley Kriegler)

  3. Algebraic Thinking It is made up of two parts • the development of mathematical thinking tools • Mathematical thinking tools include analytical habits of mind, specifically problem solving skills, reasoning skills, and representation skills. • the study of fundamental algebraic ideas. • Fundamental algebraic ideas represent a domain in which mathematical thinking tools can develop

  4. Big Ideas • Patterns • Balancing • Variables • Functional Relationships • Proportional Reasoning

  5. Patterns • Reoccurring event or objects Student patterns: • Gr. K-3-Have students line up in ABA patterns (boy, girl, boy, girl), ABBA pattern (boy, girl, girl, boy), line up my clothing patterns, use objects to make a pattern, make attribute train patterns, • Gr. 4-6 make patterns with more abstract thinking: line up in bus patterns, block patterns

  6. Balancing Definition • Making two sides equal or the same • http://www.mathplayground.com/AlgebraEquations.html

  7. Variables Definition • A symbol that represents a quantity • See Catch of the Day handout in Dr. Heilshorn’s handout

  8. Functional Relationships Definition • Is a relation between a set of inputs and a set of outputs.

  9. Function Machines Hands on Activity

  10. Proportional Reasoning Definition • The relationship between quantities The information on this site might be helpful in teaching and seeing how it is presented • http://teachmath.openschoolnetwork.ca/wordpress/grade-6/proportional-reasoning/ • We think if numbers are made to real life experiences it will make this practice easier to understand.

  11. Teaching Algebraic Thinking • Throughout the past three weeks we've learned multiple ways in which we can make math engaging and interesting. So how can we has teachers engage students in algebraic concepts. • - Technology: according to our book technology enhances and stimulates learning • - Cooperative Learning Activities: such as Showdown or Mix and Match, which are listed on p. 66 and 67 of our books • - Manipulatives: through the use of manipulatives visual learners can explore equations and patterns • - Math Literature: our book explores the concept of math literature in the classroom and recognizes how important it is. Some literature that connects to algebra is listed on a different slide. • - Personalize: anytime you can personalize the concepts do so to make a connection between the math problem and the students. • - Create Problems of the Week: like our book suggestions create problems of the week, but you could emphasize algebraic ideas.

  12. How Can You Teach It • Providing opportunity for critical thinking early is important in building a foundation for algebra in each grade. • “Marilyn Burns (2004) states that using direct instruction and memorization in a classroom is not enough; students need to create their own understanding of concepts. If they simply memorize, there is no real understanding of the procedures. One example of this idea is when students are asked to memorize the procedure for multiplying multi-digit numbers.” • Students should be required to show two ways of finding the product; this requires students to answer “an open-ended problem where students are asked to show their work in any way they would like. It addresses problem-solving skills, uses content vocabulary, and enhances their communication skills to deepen their understanding of multiplication.

  13. TeachingElementary Algebraic Thinking • “Blanton and Kaput (n.d.) urge K-5 teachers to focus on carefully selected problems that cover important mathematical ideas, can be approached at different levels, can generate conversations, involve reasoning and computation, and have a variety of ways to answer them. One well-known example is a form of the Handshake Problem (Carraher, Schliemann, andBrizuela, 2000)”

  14. TeachingMiddle School Algebraic Thinking “Communication and a community atmosphere are important components in the middle school math classroom (Pugalee, 2001). Teachers need to present students with mathematical tasks that require problem-solving skills. They need to be allowed to discuss and critique each other in a safe classroom environment. Students who are assisted with their “speaking, writing, reading, and listening in mathematics classes reap dual benefits: they communicate to learn mathematics, and they learn to communicate mathematically” (NCTM 2000, p. 60).” Strategies: Think-alouds, technology, video game (ex. Dimenxian,)

  15. TeachingHigh School Algebraic Thinking “In order to prepare students for advanced mathematics classes, instruction at the high school level should focus on three elements: communication, connection, and context (Steen, 1992). Students should be able to interpret data, calculate data, and communicate about quantitative topics (Taylor, 2007).” Strategies: Connect meaning to numbers in authentic contexts, such as in history, geography, economics, or chemistry. This allows students to authentically measure, analyze, and infer understanding (Steen, 1992). Think-alouds,

  16. Children’s Literature “Marilyn Burns (2005) urges K-5 teachers to make a connection between the way they teach reading to how they could teach math. She offers a few specific strategies that connect the two disciplines. Teachers can ask students to make estimates before solving problems, just like they ask students to make predictions when reading a story. Students can write and discuss their reasoning ideas with their peers, just like in a literature group. Teachers can also post a word chart for new math vocabulary. Finally, teachers can encourage different solutions for solving problems and presenting ideas.” Resources http://www.utc.edu/Faculty/Deborah-McAllister/tetc2005pres.htm http://www.naeyc.org/files/tyc/file/MathbookslistSchickedanzexcerpt.pdf

  17. Technology Games • K-12 Online Math Practice http://www.ixl.com/math/algebra-1 • K-12 Algebra Math Games http://www.math-play.com/Algebra-Math-Games.html • Algebra for the IPad Generation http://mathandreadinghelp.org/articles/Algebra_for_the_iPad_Generation.html • Youtube Video http://www.youtube.com/watch?v=XpoFxwKBwE8&feature=related • Additional Resources http://www.mathwire.com/archives/algebra.html http://www.mathwire.com/archives/algebra.html

  18. Resources • M. Argo, Education Service Center, retrieved from http://www5.esc13.net/cscope/cscopeconference/document/cscope_pres/2009Presentations/June24/K-5AlgebraicReasoning/K-5AlgebraicReasoning.pdf • Krieler, Shelley., Just WhatIis Algebraic Thinking? Retrieved from http://www.math.ucla.edu/~kriegler/pub/algebrat.html

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