Another fantastic day!
We began with the name game, with a total of 210 names said. We then shared our solutions to the Caterpillar problem, listing 4 different formulas and ideas for more.
We then moved into the “Gross Problem” to complicate our instincts on how place value interacts with subtraction. Solutions presented included subtracting mixed numbers and how that also draws upon similar ideas when borrowing.
Just before lunch we discussed using conceptual understanding to build procedural fluency.
After lunch we discussed the “iceberg” model, and how any topic is supported by many earlier ideas.
We then moved into multiplicative algorithms, in particular how the Partial Products (or area method) is tucked into both the standard algorithm and the lattice method.
Read Principles to Actions, the section titled “Support Productive Struggle in Learning Mathematics” (p. 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?
Watch the following videos which relate to productive struggle
Science of Thinking: https://www.youtube.com/watch?v=UBVV8pch1dM
Don’t Get Stuck: https://www.youtube.com/watch?v=VrSUe_m19FY
We began by sharing our thoughts on “Rules that Expire.” (Posters: Rules that Expire)
We then moved to the issue of equivalent fractions, “cancelling,” and how to make sense of a fraction you must make sense of “the one.”
After lunch, we first met in small groups to discuss the Principles to Actions reading from last night and then debriefed as a whole group.
We then complete the following:
- Read Principles to Actions (the blue book): 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?
Then we watched Dan Meyer’s TED talk.
Fran shared a resource for 3 Act Tasks, developed by Dan Meyer.
Next we talked about the variety of forms that addition and subtraction scenarios can take. Next we started on the Insatiable Caterpillar task, which we will wrap up tomorrow.
Math HW: Analyze the student work on Block 1, Pages 13-14. Think about the caterpillar.
- Read Principles to Actions: Section titled “Build Procedural Fluency from Conceptual Understanding” (p. 42-48).
- Also read: Webb, Bozwinkel, & Decker. Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding. MTMS, 2008. (Handout from today)
Respond to this prompt in your notebook: What connections do you see between these two readings? What questions do you have?
Here are three articles that you might find interesting to read and share with colleagues:
This post is just to say that this is the place where we will be posting summaries of each day’s topics and the homework for the next day.
Update 7/23/18: We are sorry to announce that we will need to cancel the workshop announced below due to a lack of participants. We hope to offer a similar workshop at PSU Brandywine in the fall or winter.
We are happy to announce that we are offering a 3-day workshop at Penn State Brandywine in Media PA. Participation is free, and lunch is provided, but there are only 25 seats. Participants will be chosen on a first-come-first-served basis. Participants providing their PPID can earn 18 continuing education credits. Workshops will run July 31 – August 2, 8:30am-3:30pm, with lunch provided each day.
The workshops will focus on math content from grades 5-8, and will be open to both newcomers to PMI and to those who have already participated in prior PMI workshops. Topics to discuss include:
Making sense of decimals, negative numbers, rational numbers, and irrational numbers
Using ratios, proportions, and percentages flexibly to solve problems
Mathematical modeling with linear equations
Teaching through rich problems and discussion
Leveraging conceptual understanding to build procedural fluency
Unpacking the Standards of Mathematical Practice
We are excited to announce the 2018 Summer Workshops.
- Math as a Second Language (Week 1). July 16-20, 2018. University Park.
- Algebraic Thinking and Proportional Reasoning (Week 2). July 23-27. University Park.
Participation in these workshops is free, but space is limited to 24 participants. Participants will receive 30 credit-hours per week toward continuing education (Act 48) requirements. Selected participants may also receive compensation for travel or lodging, based on need. Due to funding considerations, we do not expect to be able to provide stipends as in past years.
Selection is not first-come-first-served. Participants are chosen with the intent to balance grade bands, district need, geography, and other factors.
Applications are now open. See the 2018 Workshops page for more details and an application.
I write today to commemorate the man who inspired the Pennsylvania Mathematics Initiative: Kenneth I. Gross. Ken passed away in September, after a long life of mathematical and education contributions. Chief among the education is his founding of the Vermont Mathematics Initiative, which served as a model for PMI. When George Andrews was looking for a program that could make a difference in the quality of elementary math education, it was VMI’s content-focused approach that he found most promising.
I first visited Ken’s program in the summer of 2012 when the idea of starting a similar program at Penn State was proposed to me. He and the rest of the facilitators welcomed me with open arms, and within an hour or two I had me helping with the workshop. It was inspiring to see the excitement and enthusiasm that everyone shared, and I am happy that I have been able to capture that to bring to Pennsylvania. Ken generously offered me a chance to “run with the big kids,” so to speak, when he invited me to co-teach a week-long workshop with him and Cyndi Garvan in Levy County, Florida in 2013. This was my trial by fire, as I was to run our first PMI workshop a month later with the same materials. I remember the experience and car-trips with Ken fondly.
Ken shared his materials freely with me, for the sake the teachers of Pennsylvania, and was willing to gamble on a young buck like me to modify and rewrite large parts of them. He asked me to act as co-author for the textbook he was writing for VMI, but I regrettably could not devote the time it needed. I wish now that I could have spent more time working on it with him, even if we hadn’t finished it in time, just to have had more time to talk with him and learn from his experiences.
While I only knew Ken for five years, he has been a tremendous influence on my life and PMI in general. He always had time to talk, and took an interest in my life outside my career. He sent me congratulation cards when my daughters were born, and always spoke fondly of his own two daughters. He was a wonderful mentor, a terrific advisor, and a good friend. He absence will be felt as PMI continues in his memory.
Summer 2017 was the biggest year yet for PMI!
PMI’s growth since its first workshop in 2013. Totals account for that summer’s workshops, accrued over all sites. 2016 involved 3 sites, 2017 involved 4.
Summer 2017 at a glance:
- Workshops at 4 different Penn State campuses, facilitated by 10 Penn State faculty members
- 245 hours of instruction
- 95 participants from 37 school districts across Pennsylvania
We offer a hearty “Thank you” to all of our supporters. We could have never done all of this without the contributions from Earth and Space Science Partnership and NSF award DUE-0962792, the PSU Math Department (University Park), the Eberly College of Science, the College of Education, the office of the Vice Chancellor of Commonwealth Campuses, and the Penn State Provost’s office.
Productively struggled our way through the candle burning problems as we learned about linear relationships
Watched some videos:
- Mindset #1: https://www.youtube.com/watch?v=NWv1VdDeoRY
- Mindset #2: https://www.youtube.com/watch?v=hiiEeMN7vbQ
- Escalator: https://www.youtube.com/watch?v=VrSUe_m19FY
- 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)
We started the day with meeting the returning participants. We then moved to reviewing the homework at our tables. We proceeded to discuss some student work on the Hourglass Problem, and then the Punch Problem and attending to precision.
In the afternoon we discussed the importance of using rich problems (and keeping them rich when they meet the classroom). We then joined up with the returning participants and found out how they implemented what they’ve learned at PMI.
Make an attempt at the “Two Routes” problem, including the Going Further section.
No pedagogy homework.
This morning we dug deep into the question “How can we tell a pattern will always hold?” by revisiting the Snail problem, and then exploring the “Even and Odd” activity in Block 1.
In the afternoon we discussed the teaching practices of Pose Purposeful Questions and Elicit and Use Evidence of Student Thinking.
After the pedagogy discussion we began Block 2 and relating to proportional reasoning.
- Read either Message 14 or Message 16, based on your last name.
- Block 2, Page 3. Problems 1 and 4. Try to use as many representations of proportional relationships as possible.