Teach for Understanding Math
Introduction
In the previous units we have learned what understanding is and how generative topics can foster that understanding. This unit will focus on different strategies that can be applied during your lessons with generative topics to develop a deep understanding. With the new Common Core Standards the traditional role of a teacher can no longer be the way of instruction. It is imperative that educators create meaningful and engaging tasks for students.
Understanding mathematics does not mean to memorize recipes, formulas, definitions, or theorems.
You understand a piece of mathematics if you can do all of the following:
• Explain mathematical concepts and facts in terms of simpler concepts and facts.
• Easily make logical connections between different facts and concepts.
• Recognize the connection when you encounter something new (inside or outside of mathematics) that's close to the mathematics you understand.
• Identify the principles in the given piece of mathematics that make everything work. (i.e., you can see past the clutter.)
Effective instructional strategies within the mathematics classroom will help students to grow into life-long learners and reach their fullest potential.
Objectives
- Develop effective strategies to foster student deep understanding when presented with a classroom scenario
Tasks
Write down 3 questions you regularly ask your students during a lesson. Read the first two articles on teaching for understanding. These two articles focus on the importance of asking questions to guide students to a better understanding. After completing the readings, write an analysis on the importance of using questioning with your students. Were the questions you wrote down before the readings sufficient? Going back to the topic you thought of in Unit 1, then developed deeper as a generative topic in Unit 2, write down 5 questions you will ask your students while teaching that topic.
The next two articles focus on a variety of strategies used in the classroom. Write out 5 strategies for which you can incorporate into teaching your topic. Specifically write HOW you can apply these strategies into your lesson.
In what way do these strategies and questions foster a deep understanding within students? How will this information change the way you teach in your classroom?
Resources
Strategies to Reach All Students
Sources
Clark, S. Benjamin, Gersten, Russell. (2007). Effective Strategies for Teaching Students with Difficulties in Mathematics. NCTM, 1-2.
Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10. Portsmouth, NH: Heinemann.
Furner, J. M., Yahya, N., & Duffy, M. (2005). Teach Mathematics: Strategies to Reach All Students. Intervention In School & Clinic, 41(1), 16-23.
Wiggens, G., & McTighe, J. (2008). Put Understanding First. Educational Leadership, 65(8), 36-41.
Advance to Unit 4: Developing Lessons
Return to Unit 2:NYS Mathematics and Common Core Standards