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!
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).
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.”
We are happy to announce we will be offering our usual 2-week workshop Summer 2019.
Dates: July 15-19 and 22-26. (9am – 4pm daily)
Location: Penn State University Park Campus, McAllister Building.
See the information page for more details and an application.
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!
Read the Professionalism Section of Principles to Actions (pp. 99- 108).
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.
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”).
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.
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.
From Principles to Actions (the blue book): Read two sections:
- Pose purposeful questions (p. 35)
- Elicit and use evidence of student thinking (p. 53)
In your notebook, write a response to these three prompts:
- 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.
- 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.
- 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?
The following is a (partial) list of rich problems
Illustrative Mathematics: https://www.illustrativemathematics.org/
(many rich tasks, keyed to CCSS codes)
Graham Fletchy’s website: https://gfletchy.com/
(includes 3-act tasks for elementary grades, progression videos, and other interesting resources)
(more to come, hopefully…)