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.
What a full two weeks! And yet there always seems to be more to do.
We started the morning with the post-assessment and beliefs survey. The analysis of that data will be shared later this summer.
We then spent some time refreshing the addition and subtraction of signed numbers, and representing that with joining and taking away piles of color-coded counters. That discussion progressed into exploring the multiplication of signed numbers. We found that when one or two of the factors are positive whole numbers, then we can rely on the “__ groups of size ___” model. However, when both factors are negative we need to rely on logic and the distributive property in particular. We ultimately had three explanations: one based on patterns, one based on the notion of the opposite, and one based on comparing the products 4×4 and the expanded form of (5+(-1))x(5+(-1)).
We then split into teams of 3 to do “Bungee Barbie” and started analyzing the data over lunch. Here is the winning drop: https://photos.app.goo.gl/TJO0BwptyT0slWrm2 . After the drops, we debriefed on the mathematical thinking and topics that occurred within that task.
We then got into our “Kumbaya” circle and reflected on what we learned about mathematics, what we learned about teaching, and our commitments to how we can improve our own classrooms. We then read “Hooray for Diffendoofer Day.” The key take-away message: Teach your students to think and the tests will take care of themselves.
Continue to give your students the best educational experiences possible. Continue to learn how to make those experiences richer, and continue to seek out why of mathematics.
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.
Fran Arbaugh will be leading sessions for past PMI participants at University Park on Wednesday 7/26 and Thursday 7/27. Most of the time will be directed toward classroom practices, with some math content as time allows. There will also be times where we interact with the 2017 PMI participants.
We’ll need to limit seating to 20 participants, on a first-come-first-served basis. Apply below.
We had a great PMI workshop last week at Berks campus. We are hoping to do it again in 2018, so tell your colleagues.
Group picture at the lion statue
Talking math and liking it.
A typical problem-solving session.
It’s hard to believe our week is almost over.
Read: Principles to Actions sections on “Facilitate Meaningful Mathematical Discourse” and “Pose Purposeful Questions,” pages 29-41.
Do: “Problems on Division” Block 3, Page 37. Problems 3 and 4.
Another great day for math and education!
The link to the video we watched today is here: http://veritasium.com/education/the-uncomfortable-effort-of-thinking/
Read: The article distributed at the end of the day: “Relational Understanding and Instrumental Understanding.”
Do: Block 2, Page 26.
We are off to a great start for PMI at Berks. We have 22 participants from 7 districts, with every grade level from Kindergarten to 6th represented.
This evening’s homework is as follows:
- Read Principles to Actions pages 1-11 and pages 17-24.
- Reflect on a task you have assigned your class, and analyze it from the perspective of what level of cognitive demand it makes.
- Choose 3 categories from the “Spectrum of Subtraction” in Block 2, Page 9. For each one, write a word problem appropriate for your grade level. We will share these on Tuesday.
- Complete both “Addition and Subtraction Problems” on Block 2, Page 10.