Sunday, April 24, 2016

Highlights from NCTM!

Happy Math Awareness Month! Classworks celebrated by attending NCTM in San Francisco.

There were so many great sessions focused on supporting students with today’s math standards. Two areas stood out -- helping students justify their answers and encouraging productive math discourse. Classworks Applied Math supports you with both! 

Help Students Build Justifications

Students must be able to construct viable arguments and critique the reasoning of others. They are expected to provide mathematically sound reasoning and justification, not just demonstrate procedural fluency.

What Can You Do? 

Create a safe and positive environment and set norms for justification. Work as a class to construct justifications so students understand the thought process and aspects involved.

Apply it to Your Lessons

A few ideas suggested at the conference:

  • The Skeptic and the Convincer - Partner students and have them take turns as the skeptic and the convincer. The convincer presents the justification. The skeptic analyzes it for the necessary components, poking holes where needed. 
  • Sort Chart - Create a chart of arguments. Together, sort the arguments into weak and strong. Discuss why the argument is placed into that category. 
  • Show What You Know - Provide sample student explanations and have your students evaluate each. If they decide justification is not sound, have them edit and add components to strengthen it. Classworks Applied Math Investigative problems have two sample student responses for each activity that would be GREAT for this!

Mathematical Discourse in Your Classroom

Students must develop the ability to communicate mathematically. How do you effectively make the shift from lecturing to creating a mathematical conversation in your classroom?

What Can You Do? 

Guide the discourse in your classroom, but expect students to ask each other questions about their work. 
Have peers explain an error made to their classmates. Step in only as a last resort and follow up with the student who was incorrect during conferencing.

Apply It to Your Lessons
To facilitate a math discourse:
  • Provide enough wait time
  • Allow multiple opportunities for student-to-student talk
  • Ask students to restate each other’s ideas
  • Create a classroom culture where students are comfortable sharing ideas, and the expectation is that all students participate
Applied Math activities allow for flexibility in the way students communicate their ideas. Pro tip: Have students work together to solve one of the problems and create justifications for their answers to share with each other. Have some groups record their reasoning and others communicate visually using the canvas.   

Monday, April 11, 2016

Build Confidence and Competence in Math

How? A recent Education Week article* considers four purposes for assigning math problems to help students deepen mathematical understanding. Use Classworks Applied Math to give your students meaningful math practice that addresses each of the four areas.

  1. Learn “new” content.
“...Math teachers should strive to introduce content through problems that are accessible yet challenging for students.”

Applied Math:
Includes differentiated problems that are complex enough to engage students with productive struggle. Activities address the same standard at varying levels of difficulty. Students interact with new content at an entry point that is comfortable and appropriate for their level of understanding.

2: Deepen understanding of previous content.
“...Teachers must assign the right problems and be prepared to scaffold students’ understanding.”

Applied Math:
Provides necessary pre-requisite content standards to make vertical connections between concepts. The canvas supports scaffolding of math communication and is a platform for conversation while students develop understanding and connect to previous knowledge.

3: Reveal and resolve misconceptions.
“...Don’t prevent students’ mistakes, prepare for them.” Don’t rob students of these important learning opportunities.

Applied Math:
Supports you with resource documents for each lesson that include common misconceptions to anticipate. Plan for responses or examples ahead of time to help guide learning. Allow students to make mistakes and then review the error and ways to avoid it.

4: Develop procedural fluency.
“...Procedural fluency builds conceptual understanding, strategic reasoning, and problem solving... Assign problems that are conducive to discovering and discussing multiple solution strategies.”

Applied Math:
Helps develop procedural fluency by building skills and knowledge through the progression of differentiated problems. Problems are written to allow for multiple solving strategies using tools on the canvas and/or the audio recording tool. See it in action.

Blog post written by Lynde Taylor, curriculum specialist and former middle grades math teacher.