Math as a Second Language, Day 5 (7/14/17)

We began today by looking at how the Standard Algorithm for multi-digit multiplication rests on a foundation of the distributive property of multiplication. We also looked at how the Adjective-Noun theme applies in multiplication: when you’re multiplying, you multiply the adjectives and multiply the nouns. This will have implications for how we treat the multiplication of fractions.

Then we thought about multiplying fractions, using an area model. When we practiced, we realized that multiplying whole numbers by fractions can get a bit confusing. We need to keep careful track of what constitutes our “whole” in this case. Using the number line can help here, too.

After morning break, Nursen led a discussion of productive struggle. She showed the “My favorite no” video. During the discussion, the group generated the following:

Beliefs about Teaching and Learning Mathematics Beliefs about Teaching and Learning Mathematics
Ms. Flahive (Ms. F) Ms. Ramirez
Direct

Closed mindset

Friend to students

Makes math easier (for her & kids)

Gives explicit strategy/instruction

Delivering information

Concerned with product not process

Keeper of the information

Control—not sharing authority

Avoids frustration

Removes challenges

Task requires reasoning & problem solving

 

Facilitator (teacher as)

Encouraging work through challenges

Wants students to use multiple approaches

Building on prior knowledge

Poses purposeful questions

Class discussions/prioritize mathematical discourse

Supports productive struggle

Utilizes strengths of students

Task requires reasoning & problem solving

Access to tools (materials, manipulatives)

Valued the process

Praises effort

 

To support productive struggle in learning mathematics, teachers can:

  • create a learning atmosphere where it’s ok to make mistakes
  • monitor carefully the students’ progress
  • model their own thinking processes and their own math struggles
  • provide a variety of tools and materials
  • invite multiple solutions
  • promote student-student interaction: evaluating and critiquing others’ approaches
  • require an explanation, justification. Use “Convince me” phrase.
  • Focus on the process not the product
  • prioritize hard work over natural ability/intelligence (growth vs. fixed mindset)
  • provide suggestions to help students make progress toward the learning goal.
  • Model and Provide suggestions to students in terms of how they should communicate
  • Establish clear math goals.
  • Purposeful pairing, grouping
  • provide immediate and helpful feedback based on effort—praise effort
  • honor students’ thinking.
  • Select activities/tasks that aligns with the learning goals and provide opportunities for productive struggle

When I get stuck, I can…

  • Use something I already know (from the problem; strategies / methods)
  • Draw a picture
  • Refer to my notes / textbook
  • Use my tools / manipulatives
  • Talk to my neighbor
  • Start again / try other methods
  • Ask the teacher (Am I on the right track?)
  • Explain my thinking and ask for “What is it that I am missing?”
  • Look for key words, hints.
  • Break the problem down into smaller steps.
  • Look for similar problems that I have done in the past.
  • Use tables, graphs, charts
  • Make mistakes 🙂

After lunch, we returned for the final math block. Beth led a discussion on division and the differences between Partitive Division or Measurement Division (she calls these “Dividing to split” and “Dividing to fit”). We pointed out how Measurement division is supported by a foundation of measurement using non-standard units that kids are doing as early as Kindergarten (“How many paper clips fit in this marker?”).

(Note: Nursen pointed me at a video that goes through how Division ideas progress through the grade levels. You can see it here: https://gfletchy.com/2016/01/31/the-progression-of-division/)

Homework:

Pedagogy Homework for Tuesday:

Read Principles to Action: “Pose Purposeful Questions” (p. 35-41) and “Elicit and Use Evidence of Student Thinking” (p. 53-57)

In your notebook, write a response to these three prompts:

  1. In questioning small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations.
  2. If Nursen came to your classroom during math time, would she see you using a funnelling pattern of questioning or a focusing pattern of questioning?
  3. Suppose a student presented you with the following piece of work. What questions could you ask that would elicit the student’s thinking?

Screen Shot 2016-08-03 at 2.22.52 PM

Leave a Reply

Your email address will not be published. Required fields are marked *