Author Archives: Andrea McCloskey

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 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?

 

Daily Recap: Week 1 Friday

We began by continuing our discussion of division with fractions. We drew pictures and looked for patterns in an effort to understand why it works to “invert and multiply.”

Then we reflected on the reading about “Upside-Down Teaching,” and brainstormed ways to shift from I-We-You approaches to You-We-I approaches.

We had time to plan for this shift by looking at curricular materials and plans for the first few weeks of school. We watched a video of the “My favorite no” practice.

We ate a delicious lunch together and some of us said good-bye to Fran. Sadface.

After lunch, Melina shared recommendations for the OGAP frameworks. Thanks, Melina!

We resumed work on operations with fractions. This time we pushed ourselves to develop even deeper understandings of the “invert and multiply” procedure.

 

PMI@UP Day 9 2017

Today we

Productively struggled our way through the candle burning problems as we learned about linear relationships

Watched some videos:

  1. Mindset #1:  https://www.youtube.com/watch?v=NWv1VdDeoRY
  2. Mindset #2: https://www.youtube.com/watch?v=hiiEeMN7vbQ
  3. Escalator: https://www.youtube.com/watch?v=VrSUe_m19FY
  4. My favorite NO: https://www.teachingchannel.org/videos/class-warm-up-routine

Worked in grade level groups to made a big iceberg poster about linear relationships. How do the concepts we teach at each grade level build floating capacity for engaging with the candle burning problem?

Discussed parents and families, using the message from Cathy Seeley’s book.

Discussed negative and positive numbers.

For tomorrow, please:

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

PMI@UP Summer 2017 Day 6

Today we

  1. Moved onto the algebraic thinking units
  2. Discussed basic facts, drills, and timed tests (see the messages we generated, below). Here is the website Andrea shared that provides opportunities for selected practice opportunities for fluency development
  3. Discussed calculators in the math classroom
  4. Interviewed a classmate for tonight’s homework

Here are some websites with calculator lessons and activities:

  1. The Math Tools website (http://mathforum.org/mathtools) allows you to search by grade level and by the type of technology you wish to use.
  2. Texas Instruments has a collection of calculator activities to review (http://education.ti.com/ calculators/downloads/US/Activities/).
  3. Casio has several calculator activities to review for elementary and middle school (http://edu.casio.com/support/activity/).

Here are our messages to ourselves about basic facts:

  • More work on strategies and practicing the strategies BEFORE drilling
  • When a 9th grader is struggling, provide tools for remediation (teach strategies!). It’s not enough to say “learn them!”
  • Timed tests are required by my district—use it as a learning tool (and assessment). Assess for individual fact families and find out what strategies they do/don’t use
  • Some facts are more powerful than others
  • Timed tests frustrate the struggling students even more and reward the quick thinkers
  • “you’re competing against yourself, not each other”—emphasize personal growth (chart for themselves)

BTW: Here is a nice website about number strings.

For tomorrow, please

Read Principles to Actions. “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. 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?

Try the Maze Playing Board. Let’s see who has the largest value tomorrow. There MAY be a prize involved.

 

 

PMI@UP Summer 2017 Day 5

Today we

  1. Drew pictures and solved problems related to fraction multiplication and division
  2. Discussed strategies for learning basic facts (addition and multiplication)
  3. Continued yesterday’s planning work in grade-level teams

For homework, please

Read from the “Elementary and Middle School Mathematics” handout:

  1. pp. 158-159 (Drill of Efficient…”), and
  2. pp. 174-end (Effective drill…”)

PMI@UP Summer 2017 Day 4

Today we

Talked A LOT about the dot problem

Generated a list of ideas about how to support productive struggle (using Ms. Ramirez and Ms. Flahive as examples):

  • Have your room set up for collaboration
  • Set the climate for day 1
  • Celebrate mistakes (my favorite mistake)
  • Use “can you catch my mistake” problems – Identify my “not yet” – analyze my answer – oops
  • Be honest with kids – tell them what you are doing and why.
  • Acknowledge that learning math/thinking is hard, but we can do it.
  • Practice makes progress, not perfect
  • Build stamina; start where they are; “Think” stage – start with a few seconds and then build up.
  • Ask students to make a plan before starting “solving”
  • Decorate your room with people who succeeded after “failing” several times.
  • Have “hip pocket” responses “what are you thinking?”
  • Figure out where kids might have struggles with the task.
  • Stop talking so much.
  • Make sure you have manipulatives available
  • Have anchor charts

Broke up into grade-level groups and began planning a “first-day lesson” by anticipating student responses

For tomorrow:

Read the Message called “Upside-down teaching”

In your notebook, complete respond to the discussion prompts for teachers at the end of the message (on p. 94). Try to make connections about what we’ve read about and discussed so far in PMI.

Many thanks to Kimberly for baking some delicious chocolate zucchini bread. Her recipe is below. (Bonus question: If you only want to make a half a loaf, how much shredded zucchini do you need? Write the number sentence to describe that scenario.)

PMI@UP Summer 2017 Day 3

Here’s what we did today

  1. Discussed last night’s “gross problems” (and made connections to kids’ struggles with place value concepts)
  2. Examined a variety of strategies for solving addition and subtraction with multidigit numbers (“alternative algorithms”)
  3. Watched Dan Meyer’s TED talk: Math Class Needs a Makeover and discussed some of the “yeah, buts…” that emerged for us
  4. Made “Iceberg posters” for procedures at each of our grade bands (see the picture below)
  5. Generated a list of reasons to put conceptual development before procedural development:
  • helps with retention
  • helps with flexible use of #s
  • rushing to fluency can cause anxiety and “bad” feelings about math
  • builds on students’ prior knowledge
  • conceptual dev. serves as a check for computationshttp://veritasium.com/education/the-uncomfortable-effort-of-thinking/
  • in the real-world, problems are more likely to be more conceptual than procedural

We also watched the video about “The uncomfortable effort of thinking.”

Here’s what’s due for tomorrow

Read Principles to Actions, the section titled “Support Productive Struggle in Learning Mathematics” (pp. 48-52). In your notebook, write a response to this prompt:

Review the “Beliefs about teaching and learning mathematics” chart (p. 11, Obstacles). What beliefs are evident in Ms. Flahive’s and Ms. Ramirez’s classrooms (see fig. 21 on page 51)? What impact do those beliefs have on students’ opportunities to grapple with the mathematical ideas and relationships in the problem?

PMI@UP Summer 2017 Day 2

Here’s what we did today:

Handshake problem: Solved it, watched 3rd graders work on it

Discussed addition and subtraction and the spectrum of scenarios that are addition and subtraction problems.

Discussed Levels of Cognitive Demand. (Addition strings and watching a 1st grade classroom)

We began our discussion of adjective-noun theme.

Here’s what’s due for tomorrow:

Read Principles to Actions: Section titled “Build Procedural Fluency from Conceptual Understanding” (pp. 42-48).

Also read: Webb, Bozwinkel, & Decker. Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding.  MTMS, 2008.  (Handout from class today)

In your notebook: Identify a procedure or skill that you consider essential for students at your grade level to learn. List the conceptual understandings that support students’ learning of the procedure or skill.

Write questions you have about the readings.

Write three problems illustrating different categories of addition and subtraction, as outlined from Block 2, page 8 “you try.”

Work through “Two Gross Problems” in Block 4, page 6.

PMI@UP Summer 2017 Day 1

Here are the definitions of the Strands of Mathematical Proficiency that were in the PowerPoint today:

Adding it Up: Helping Children Learn Mathematics, National Research Council (2001, p. 116).

  1. Conceptual Understanding – comprehension of mathematical concepts, operations, and relations.
  2. Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.
  3. Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification.
  4. Strategic Competence –  ability to formulate, represent, and solve mathematical problems.
  5. Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

This book can be downloaded for free at this link.

Homework

Read Principles to Actions (the blue book):

  1. Sections titled Progress and Change; Effective Teaching & Learning (Pages 1-12)
  2. Section titled “Implement Tasks that Promote Reasoning and Problem Solving” (pages 17-24).

Write answers to the following prompts in your journal:

  • Reflect on a typical in-class math lesson (use your textbook to refresh your memory). Using the descriptions of Levels of Cognitive Demand in Figure 3 (p. 18), describe the types of mathematical thinking your students are required to engage in during a typical lesson.
  • Reflect on a typical homework assignment that your students complete (use your textbook to refresh your memory). What level of cognitive demand do most of the tasks on a typical homework require of your students?
  • Consider the chart about beliefs on page 11. What is your reaction to this description of unproductive and productive beliefs?

Read through and reflect on the 8 Rules that Expire.

  • When does the rule work?
    • Bonus: What grade level does that scenario occur?
  • Give a mathematical scenario where the rule does not work (at least, not in the way it’s phrased)
    • Bonus: What grade level does that scenario occur?