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SUMMARY
Every student has a teacher with appropriate mathematics content knowledge and the knowledge for teaching mathematics. Math lessons are rooted in a solid understanding of the standards through rigorous, high-quality curriculum and meaningful tools.
Examples
Teacher math knowledge for teaching: subject matter knowledge AND pedagogical content knowledge
Aligning and unpacking major standards
Integrating ELD standards into every lesson
Physical needs
Vertical non-permanent surfaces
Math Technology - GeoGebra, Desmos, IWB, etc
Rigorous curriculum
Deep Dive
In Maslow's hierarchy, the bottom layer addresses the physiological needs such as breathing, food, water, shelter, etc. Without fulfilling these needs a person will have little chance of thriving and advancing to the next level. In the Math Hierarchy of Needs, the bottom layer is called Material Needs.
Material Needs begins with the knowledge that for students to develop a deep understanding of mathematics they must experience a steady stream of effective math teaching practices. Building on Deborah Loewenberg Ball's 30-year study of effective math teaching practices, teaching well requires teachers to have a specialized type of knowledge called Mathematical Knowledge for Teaching (MKT). MKT includes abilities such as analyzing the student thinking that led to an incorrect answer, identifying the mathematical understanding a student does not yet have, and deciding how to best represent a mathematical idea so that it can be understood by students.
Teachers need to strengthen their math content knowledge for the purpose of making math accessible for students. More than arriving at the correct answer, can the teacher use concrete manipulatives, pictorial representations, or numbers and symbols to illustrate for students WHY the answer is what it is...not just HOW to get the answer.
Teachers also need to increase their understanding of how students learn mathematics. For a given math concept, which visual representation might provide the biggest bang for the buck? Is there a solution strategy that might support students beyond just the current math concept, but also scales up to subsequent topics.
Lastly, can teacher implement instruction strategies that promote thinking, reasoning, and making sense of mathematics. There are a variety of such strategies: Thinking Classrooms, 5 Practices, Teaching through problem-solving, and Three-Part Lessons are examples.
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