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.
- Moved onto the algebraic thinking units
- 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
- Discussed calculators in the math classroom
- Interviewed a classmate for tonight’s homework
Here are some websites with calculator lessons and activities:
- 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.
- Texas Instruments has a collection of calculator activities to review (http://education.ti.com/ calculators/downloads/US/Activities/).
- 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:
- 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?
Try the Maze Playing Board. Let’s see who has the largest value tomorrow. There MAY be a prize involved.
- Drew pictures and solved problems related to fraction multiplication and division
- Discussed strategies for learning basic facts (addition and multiplication)
- Continued yesterday’s planning work in grade-level teams
For homework, please
Read from the “Elementary and Middle School Mathematics” handout:
- pp. 158-159 (Drill of Efficient…”), and
- pp. 174-end (Effective drill…”)
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
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.)
Here’s what we did today
- Discussed last night’s “gross problems” (and made connections to kids’ struggles with place value concepts)
- Examined a variety of strategies for solving addition and subtraction with multidigit numbers (“alternative algorithms”)
- Watched Dan Meyer’s TED talk: Math Class Needs a Makeover and discussed some of the “yeah, buts…” that emerged for us
- Made “Iceberg posters” for procedures at each of our grade bands (see the picture below)
- 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?
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.