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A Problem-based Curriculum. College Preparatory Mathematics. Tom Sallee University of California, Davis. Outline. How do we get more students to learn algebra 1? Math Goals. Attitude Goals. Learning Approach. Examples of how approach was implemented.

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## A Problem-based Curriculum

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**A Problem-based Curriculum**College Preparatory Mathematics Tom Sallee University of California, Davis**Outline**• How do we get more students to learn algebra 1? • Math Goals. Attitude Goals. • Learning Approach. • Examples of how approach was implemented. • How did we approach writing the books? • Lessons learned. • If you want to try this yourself. • Questions Rigorous • Aligned • Balanced • Accessible**CPM Fast Facts**• CPM has developed curriculum for 19 years. • Is a non-profit organization, and has curriculum for grades 6 through 12. • Was started with an Eisenhower grant… not NSF • Written by 6-12 teachers, mostly from California • Was heavily influenced by the 1985 and 1992 California Frameworks and the 1989 NCTM Standards • Has evolved significantly Rigorous • Aligned • Balanced • Accessible**Primary Focus**Getting more students to learn algebra 1, retain their knowledge, and be able to transferit, not just “cover the material”. Originally the first year of a three-year sequence. Rigorous • Aligned • Balanced • Accessible**Central Issue**Difficulties of most students are more about Learning than about Mathematics Rigorous • Aligned • Balanced • Accessible**Math Goals for Students**• Understand the Big Ideas as a connected set of concepts • Be able to move among different representations of the same concept: written, tabular, graphical, symbolic. • Use Problem Solving techniques as both a solution tool and a learning tool Rigorous • Aligned • Balanced • Accessible**Attitude Goals for Students**• I can figure out most problems without being told by the teacher. • I want to learn math. • I want to understand what I learn. Rigorous • Aligned • Balanced • Accessible**Big Ideas**• Representing functions with equations, graphs, tables, and contextual situations, and making connections among these representations. • Writing equations from contexts (word problems) • Solving equations, systems of equations, and inequalities • Symbolic manipulation, using equivalence • Proportionality Rigorous • Aligned • Balanced • Accessible**Learning Approaches**• Math is not a spectator sport Work matters. Engagement matters. • Solving problems is the best way to learn new ideas. • Talking about mathematics with others will help you understand new ideas. • Connecting abstract concepts (like factoring trinomials) withconcrete experiences (like manipulating building rectangles with algebra tiles) helps integrate your knowledge. Rigorous • Aligned • Balanced • Accessible**Learning Approaches**• You will retain ideas better if practice is spaced over weeks or months • It takes a long time to learn a big idea. • There are mathematical ways of thinking (such as generalizing, justifying, connecting) that take time and practice to develop. Rigorous • Aligned • Balanced • Accessible**Multiple Representations**Rigorous • Aligned • Balanced • Accessible**Use of Algebra Tiles**Symbolic manipulation is developed through use of concrete tools • “Legend” reminds students and teachers which tiles are positive and negative • “Minus” region negates the tiles in that region, helping students represent the opposite of a negative. Rigorous • Aligned • Balanced • Accessible**Intro to simultaneous equations**Rigorous • Aligned • Balanced • Accessible**Student tasks for problem**Rigorous • Aligned • Balanced • Accessible**Guidance as necessary**Rigorous • Aligned • Balanced • Accessible**Introduction of a new idea**Rigorous • Aligned • Balanced • Accessible**End of the problem**Rigorous • Aligned • Balanced • Accessible**Setting up equations**A rectangle is 3 cm longer than it is wide and has a perimeter of 54 cm. What are its dimensions? Write an equation that will allow you to solve this problem. Rigorous • Aligned • Balanced • Accessible**Setting up equations**A rectangle is 3 cm longer than it is wide and has a diagonal of 30 cm. What are its dimensions? Write an equation that will allow you to solve this problem. Rigorous • Aligned • Balanced • Accessible**How did we approach writing the book?**• Constrained optimization problem. • Have talked about math goals and attitude goals for students. • What were constraints? Rigorous • Aligned • Balanced • Accessible**Constraints**• Assumptions need to be made about • Students • Teachers • Schools • States • Parents Rigorous • Aligned • Balanced • Accessible**Examples of our Assumptions**Students Most think math is something to be memorized. Many of those we are most anxious to reach will not have a place to do homework. Teachers A course that requires more work will not be kept. Rigorous • Aligned • Balanced • Accessible**Examples of our Assumptions About Constraints**Schools Generally a new program must co-exist with the old. States Standards, frameworks, accountability. Parents (Mostly parents of high-ability students) I need to be able to help my child. There needs to be plenty of practice. Rigorous • Aligned • Balanced • Accessible**Generation 2Algebra Connections**• Major differences • Clearer storylines of the mathematics • More transparent daily structure--eg what is homework? • Made the mathematical goal of problems, lessons, and chapters explicit. • Teacher has the option of presenting problems with less scaffolding, so teamwork is more necessary. • Much more extensive teacher notes Rigorous • Aligned • Balanced • Accessible**Biggest Things We Learned**1. Can’t just write a book with a new approach Need LOTS of professional development to go with it. Current model--eight days (free) inservice for each course plus classroom visits 2. Politics matters. 3. In judging effectiveness, facts matter a lot less than personal prejudices. Rigorous • Aligned • Balanced • Accessible**If you want to do this yourself**• Think very hard about the students for whom you are writing the books and your goals for them. • Trust yourself on the math. • Trust teachers on pedagogy. Don’t ever think you know more about what will work in a classroom than a good teacher. • Go sit in classrooms and find out what the reality is before you begin. • Iterate your efforts. Rigorous • Aligned • Balanced • Accessible**Get Involved in K-12 Math**• There is a need, • There is funding, and • It is the most fun you will ever have. Rigorous • Aligned • Balanced • Accessible

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