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Blog Recap: 2019 Day 8

Today we talked about unit rates (and representations thereof) based work with the Coffee Maker problem and the Perfect Pint of Pink Paint. See the image below.

Then after lunch, we discussed the reading about “access and equity” from Principles to Actions. We discussed productive vs unproductive beliefs, we played with the scenario cards, and we connected all of that with

  • the 5 strands of mathematical proficiency
  • the Standards for Mathematical Practice
  • The Effective Teaching Practices

Then we solved the Hourglass problem, and compared student work thereon.

Tonight you are invited to pre-read your assigned “message” reading. These were distributed at the end of class.

Have a good night and see you tomorrow!

 

Blog Recap: 2019 Day 7

This morning we spent learning about why the integer (positive and negative numbers) operations work! We talked about adding, subtracting, and multiplying signed numbers – ultimately learning why a negative number times a negative number is a positive number!!!

We then embarked on solving the Kayak problem. After lunch, we continued with the Kayak problem before moving on to pedagogy.

During the pedagogy time today, we read Cathy Seeley’s message titled “Upside Down Teaching” and talked about positive reactions to the message and challenges with teaching in this way. We then did the “Planning for Implementing High-Level Tasks” activity.

For those who want to reread, tomorrow we will be reading and discussing the Access and Equity section in PtoA (p. 59-69).

Blog Recap: 2019 Day 6

In the morning, we welcomed new teachers and started thinking algebraically! We revisted Otto and Hannah (Sibling Rivalry: Unknown Quantities), but this time they were eating Halloween candy, comparing heights, and running!

After lunch, we learned about performance and learning goals (Band Concert Task) and revisited how to use goals to support asking assessing/advancing questions (like we did last week with the Brownie Problem). We then did an activity where we analyzed a set of student work (Walking from School Task) and discussed how goals can support selecting, sequencing, and connecting student work in mathematical discussions (see page 30 of PtoA and the entire section on Facilitate Meaningful Mathematical Discourse). Fran ended the session with this diagram, which shows how goals can inform all of the other 7 PtoA teaching practices:

We ended the day with the “Back and Forth along Euclid Avenue” task – exploring positive and negative numbers! We then did Block 1, page 4 “Adding and Subtracting Signed Numbers via the Number Line.”

Blog Recap: 2019 Day 1

We had a great first day!

We began with our first problem, the Star Spangled Banner Problem.  Participants shared a variety of solution methods using patterns found in numerical tables, patterns in the drawings of the stars, and also using functions.

We did the Two Gross problems and discussed the adjective-noun theme, and then we did some fraction problems in which we “messed with the whole.”

After lunch, we discussed “Smarter than We Think” (by Cathy Seeley). We developed a list of phrases to use instead of “You are smart”

We watched 2 videos about Carol Dweck’s research on fixed vs. growth mindsets, and we also watched a video of a classroom routine called “My favorite no.” Below is a picture of books that were shared and recommended:

We ended the day with a discussion of the Sibling Rivalry problems and the “Adjective Noun Theme,” which is based on the notion that numbers are most useful when they are considered with context.  Numbers are adjectives describe the amount of some noun.  We then tried to apply this viewpoint to compare similar fractions, treating the denominator as a noun and the numerator as an adjective.

Math HW:

Do the “Evening Reflections” from Day 1 of the blog. Respond to these in your notebook. You don’t have to completely solve every one!  Just come tomorrow morning having about them.

Pedagogy HW:

Read Principles to Actions (the blue book):  Sections titled “Progress and Change” and “Effective Teaching & Learning”(Pages 1-12)

  • What did you learn from reading the “Progress and Change” section about the state of mathematics education in the U.S.? Write a couple of thoughts in your notebook.
  • Think about: How did you react to the chart of beliefs on page 11? In your notebook, write a reflective response (a few sentences) to the beliefs chart.

Bring a unit of your math curriculum materials (or textbook) tomorrow.

Daily Recap: Week 2 Thursday (7/26/18)

Today we began by discussing the Coloring Fun! (yellow-red-blue patterns) “Burning the candle” problems.

After lunch we made a giant iceberg poster representing how ideas at each of our grade levels build floating capacity for understanding linear relationships such as those in the candle burning problem.

Then we spent some time exploring and sharing resources we found on the NCTM website with our new memberships!

Then we talked more about other kinds of relationships between quantities besides proportional: linear and non-linear alike!

For homework:

Read the Professionalism Section of Principles to Actions (pp. 99- 108).

 

Daily Recap: Week 2 Wednesday (7/25/18)

We started the day with a long discussion of adding and subtracting fractions and mixed numbers with different denominators.  This was built on the same principles of renaming that serve us well when working with differing units and place value.

We then looked over the mathematics homework from the night before on the Purple Punch problem and shared the variety of solutions at our tables.  We then worked through a 3-act math task (Nana’s chocolate milk) and then started on the sequence of problems on currency conversion.

After lunch, Andrea and Fran led a session grounded in the brownie problem (7 brownies shared with 4 people). We developed learning and performance goals for the task. Then we read about assessing and advancing questions, examined student work for the brownie problem, and developed assessing and advancing questions for those students.

We then got is small groups and shared about the readings last night (messages 14 and 16) about “Effectiveness and Efficiency” and “Letting it Go.” We had a good whole group talk about these two messages.

We ended the day with some light mathematical coloring according to a described pattern.  The goal is to create a procedure by which we can quickly determine the color any given number will receive.

Homework: No pedagogy homework for Thursday.  Math homework is to continue to analyze and record your observations about the coloring problem.

Daily Recap: Week 2 Tuesday (7/24/18)

Today was our field trip to Chambers Building!

This morning, we began our discussion of ratios in earnest.  We began with the coffee problem, then moved into the “Perfect Pint of Pink Paint” problem.  Through these we could see how ratios can be represented in multiple ways, as well as how ratios interact with multiplying by a little more and adding a little more.

Before lunch we welcomed Dean David Monk and Associate Dean Greg Kelly from the College of Education.

After lunch we discussed the patterns in our own questioning that we heard in our teaching recordings. We watched a video clip of an 8th-grade teacher working on the “Two Tanks” problem and analyzed her questioning.

Here is the list of question stems Fran promised to share.

For a caricature of funneling questions, see this short: https://www.youtube.com/watch?v=KdxEAt91D7k

Andrew showed another way to think about multiplication with integers, and we ended the day doing more proportion problems (“the perfect pitcher of purple punch”).

For homework:

Read whichever short message was handed out to you in class today. (Either “Let it go” or “Effectiveness and efficiency”).

Revisit the “Perfect pitcher of purple punch” A-E in light of Laura’s bar model and a table-based approach.

Daily Recap: Week 2 Monday

This morning we began by discussing algebraic reasoning and reasoning with patterns. We used the Sibling Rivalry problem to illustrate how we can reason around an unknown baseline.

We then discussed modeling positive and negative numbers using a number line, addition and subtraction on that number line, and then we used colored chips to do the same. Thanks, Derrick!

After lunch, we discussed timed tests and teaching basic facts. We read together from this selection from Van de Walle, Karp, and Bay-Williams. Andrea recommended two articles from Teaching Children Mathematics: one about assessing basic facts by Kling and Bay-Williams, and  one about the importance of thinking by Buchholz.

PEDAGOGY HOMEWORK:

From Principles to Actions (the blue book): Read two sections:

  1. Pose purposeful questions (p. 35)
  2. Elicit and use evidence of student thinking (p. 53)

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. Listen to your audiorecording from today. Use fig. 14 on p. 36 and fig. 16 on p. 39 to write a description of your question patterns.
  3. How might you change your questioning to elicit and then use evidence of your students’ thinking to move the student forward to the mathematical goal of the problem?