What do we mean by "Learning with Understanding": Lesson 1

From: www.pixgood.com

Introduction

Before we move into any other class discussions, it is important to know what it means to learn with understanding. According to Carpenter and Lehrer, "Unless students learn with understanding, whatever knowledge they acquire is likely to be of little use outside of the classroom" (1999). In the early years of formal education, students learned exclusively by direct instruction. It was more teacher-centered rather than student-centered. Today, research has shown that this is not enough and my theory is that teachers who favor direct instruction force students to learn by memorizing teacher practices.

Students who are memorizing lessons are not usually learning. Typically, these students will struggle to make sense of the content and understand the procedures they copied from the board. Sometimes these students will perform well on tests but without the opportunity to explore the lesson, make connections to prior material, and reflect on the process, it is difficult for learners to create meaningful knowledge to use outside of the classroom. In the 21st century, learning is more about asking and analyzing questions, collaborative learning, and “experiencing” content rather than memorizing content.

By the end of this lesson, participants will be able to answer and reflect on the following questions:

• What does it mean to teach/learn with understanding?
• What are the advantages of teaching/learning with understanding?

Assignment

Read Chapter 2: "Teaching and Learning Mathematics with Understanding" by Thomas P. Carpenter and Richard Lehrer pp. 19-32 (1999). (In Classrooms That Promote Understanding edited by Elizabeth Fennema and Thomas A. Romberg. Mahwah, NJ: Erlbaum. Accessed via books.google.com)

• Link to Carpenter and Lehrer: https://books.google.com/books?hl=en&lr=&id=acqQAgAAQBAJ&oi=fnd&pg=PA19&dq=learning+with+understanding+mathematics&ots=Kk7xkrNl91&sig=bMoLocizdULHP9GVzbmy58kgN0E#v=onepage&q=learning%20with%20understanding%20mathematics&f=false

Reflection As you are reading, think about what is means to learn with understanding. In a two paragraph reflection, explain the advantages of teaching and learning with understanding. Use the discussion page for Lesson 1 to share your reflection. (I encourage you to read the other reflections posted in the discussion tab but you do not have to reply to other participants during reflection activities.)

Resources and References

Carpenter, T. and R. Lehrer. (1999). Chapter 2: "Teaching and Learning Mathematics with Understanding." From: Classrooms That Promote Understanding edited by Elizabeth Fennema and Thomas A. Romberg. Mahwah, NJ: Erlbaum. (Accessed via books.google.com). pp 19-32.

Links

Next Lesson: What do we mean by "Learning with Understanding": Lesson 2

Back to Unit 1: Unit 1: What do we mean by “Learning with Understanding”?

Mini-Course: Using Visualizations to Teach Mathematics with Understanding (Spring 2015 Mini-Course)

Portfolio Page: Melissa Connor's Portfolio Page for Spring 2015 Mini-Course