New: Recommendation system for PMI applicants

To guide our decision-making process, we’re introducing a way for past PMI participants and school leaders to recommend colleagues to participate in the summer PMI workshops.  Note that a recommendation for a colleague is not a guarantee they will get selected to participate this summer, and a recommendation is not required to be selected.

Fill out the form below to recommend a colleague for the Summer PMI Workshops.

PMI Colleague Recommendation

  • We may need to contact you to ask for further information.
  • If yes, specify the year and location.
  • You may fill out this form multiple times to recommend multiple applicants.

Announcing: The PMI Summer 2017 Workshops

We are ready to announce our Summer 2017 PMI Workshops at University Park.

The workshops will run Monday through Friday, July 17-28, at the University Park Campus.  Workshops are designed for current K-5 teachers and school leaders.  Participation is free, although seating is limited.

Additional details to follow soon.  Applications will open Friday, February 3.

Spring 2017 Workshop at Berks Campus

We are welcoming new applications for our Spring 2017 teacher professional development workshop at Penn State Berks campus.

Date: Thursday and Friday, March 9 and 10, 2017
Time: 9:00AM – 4:00PM
Location: Penn State Berks, Room Gaige 121
Topics: The Spectrum of Addition and Subtraction (March 9) and New Perspectives on Multiplication and Division (March 10)
Compensation: 6 hours of Act 48 credits for each day
Cost: Participation is free; lunch and coffee provided
Participants: Current K-6 teachers responsible for math instruction in their classroom, as well as math specialists and school leaders
Workshop Leaders: Dr. Andrew Baxter and Dr. Hartono Tjoe

Please register below.

Update 3/2: Registration for the Berks workshops is now closed.

Follow-up Workshop: 3/30/17

We will be hosting a follow-up workshop for all previous PMI summer workshop participants on Thursday, March 30, 2017 at the University Park campus.  Registration is at the end of this post.

Andrew Baxter and Fran Arbaugh will be running the session.  We will be discussing the following:

  • Impacts that PMI has had on your students and your colleagues.
  • Mathematical discussion on geometry in the elementary grades, and the “wall” in 4th grade.
  • Pedagogy discussion from Principles to Actions.

The workshop will run 10am-3pm, with breakfast provided started at 9am and a working lunch.

If you will be unable to attend in person but would be interested in teleconferencing, contact Andrew (  If there is sufficient interest we can set something up.


The Fall 2016 Berks PMI Workshops

Andrew Baxter and Hartono Tjoe will be presenting three Saturday workshops at Penn State Berks for K-6 teachers and math specialists.  Participation is free, and participants will receive six Act 48 credits and free lunch.

Workshops will be held Saturday October 29, Saturday November 19, and Saturday December 3.  The three workshops are stand-alone, so don’t worry if you can only make one or two.

For more information, or to apply, visit:

Summer 2016 Workshops Concluded

This has been a very exciting summer for PMI!

The summer workshops have now concluded at all three campuses.  A longer post should follow by the end of August that includes quotes from participants, photos from the workshops, and some of the quantitative data.  We worked with 75 teachers from across Pennsylvania

Until the full review, here is a map where each pin represents a school building  with a PMI participant (Thanks, Lisa!).

Each pin represents a school where a PMI participant has taught. By Lisa Krol and  Click for an interactive version.

Each pin represents a school where a PMI participant has taught. By Lisa Krol and Click for an interactive version.

Day 5 of Functions & Algebra (7/29/16)

We started the morning with Andrea and Fran sharing resources. Andrea showed the Google Folder titled PMI 2016 Resources for Participants. Then she showed the NCTM website, and discussed benefits of membership (remember that K-8 institutions get a great deal!!). This segment ended with Andrea and Fran sharing some books (here are the covers):


Andrew and Matt spent a brief time discussing Unit FA-4 on Functions, which are really just a formalization of the Processes from FA-1 with a new notation.  We then dipped into the Fox’s Furniture Store sequence from FA-5, both from the perspective of solving problems and evaluating students work on its mathematical merits.

Next we formed a large circle where Fran led a discussion about the readings on Professionalism from Principles to Actions.

After lunch, the group took the post-test (a necessary evil).  After that wrapped up Andrew and Matt tied up some loose ends and lingering questions: the Chipmunk formula from Wednesday’s homework, a strategy for solving the Milk Problem, and a justification for the “add the digits” trick for recognizing multiples of 9

It has been a fantastic two weeks!  We will be writing a longer post later with a full summary of these workshops and the workshops at Greater Allegheny and Brandywine as well.


Keep up your enthusiasm.  Seek change, and be patient.

Keep the commitment you made to yourself as you progress through the school year.

Don’t shy away from digging for the why of the mathematics you teach.  It all hangs together to form a cohesive whole.  You are welcome to send burning mathematical questions to Andrew.

Look for good candidates to recommend to PMI next summer.

Keep us updated on any revelations or experiences in your classroom that you can attribute to PMI.

Day 4 of Functions & Algebra (7/28/16)

Today we began with a discussion about the symbolic rules that describe the tortoise and hare problem. Fran emphasized that writing symbolic rules can be supported by working through the reasoning in other representations. Andrea shared some data about young children’s misunderstandings of the meaning of the equal sign and practices to avoid. We also watched a video of a young child using relational thinking to solve an open number problem.

We worked on the candle burning problem, which illustrates how a negative rate of change effects a linear relationship. After debriefing, Andrew talked through consequences of linearity.  We ended the morning with analyzing 12 situations to determine whether they could be solved via a linear relationship, a proportion, or neither.

After lunch we wrapped up some of our big pedagogy ideas by reflecting on last night’s messages, generating a list of things that need to happen in order to implement the strategies. We discussed more about the Standards for Mathematical Practice , focusing especially on supporting students to persevere.

We constructed a big iceberg wall together, representing ideas at each grade level that 20160729_104509contribute floating capacity to the concept of linear relationships.


We closed with a debriefing of the 12 situations on “What isn’t a linear relationship?” and highlighted the important features that distinguish them from each other.

See you tomorrow for our last day together!


Pedagogy: Read the section on Professionalism in Principles to Actions (pp. 99- 108).

Math:  None.

Day 3 of Functions & Algebra (7/27/16)

We are hip-deep in linear relationships (and a few things that aren’t).

Gallery Walk

We started the morning with posting some of the extension problems that participants wrote last night and then did a gallery walk.  Andrew highlighted two strategies for getting students to move to systematic or efficient strategies: using uglier numbers that are less prone to “I just knew it,” and multi-step problems where the task requiring the strategy is repeated multiple times and is part of a larger whole.

The Milk Problem

Then Andrea, Matt, and Andrew led a discussion of the milk problem, trying to make 2% milk from 1% milk and 4% milk.  A mathematical take-away lesson is “proportions don’t add, but amounts do.”  A meta-cognition lesson is “sometimes you just need to try something to see why it doesn’t work.”

Currency Conversion

Then Andrew continued the Currency Conversion problem, where now there is a fee involved.  We drew a lot of nice lessons out of it already:  parallel lines correspond to lines with the  same slope, the conversion rate corresponds to the slope of the line, the benefits of writing both fee-schemes as “convert to euros then subtract fee.”

Upside down teaching, real-world problems

We then moved into a pedagogy session, where we began with a discussion of the rich problems teachers developed during HW. Then each table generated a list for tomorrow’s iceberg activity (also from HW prompt). We also had a discussion of upside down teaching (from last night’s reading). Finally, we watched Dan Meyer’s TED talk.

Andrew shared the site which has mathematically rich games and puzzles that students will happily engage in.

Terminology for Linear Relationships

Matt led a discussion putting names (slope, y-intercept, x-intercept) to concepts identified in the Currency Exchange with Fee problem.

The Tortoise and the Hare

We looked at the Tortoise and the Hare problem, wherein a scenario is presented and participants had to ask for certain information (e.g., the speeds) and not just handed it from the start.  Table-groups were then given different follow-up questions and asked to present their answers to the rest of the group.  Along the way we saw how many natural questions can be answered via a graph.

We finished the day be repeating the teaching episodes from Monday, but now practicing purposeful questioning and eliciting student thinking.

Homework for tonight:


Write formulas for the Tortoise and the Hare problem that can answer this question: After x minutes, how many feet has the tortoise/hare/chipmunk run?  The following information was provided during class:

  • In the first minute the tortoise ran 1200 feet
  • In the first minute of running the hare ran 3000 feet.
  • The tortoise and hare maintain a constant speed.
  • The hare starts with a 10 minute nap, then runs.  The tortoise starts right away.
  • (Follow-up #7): A chipmunk starts from 12,000 feet behind the tortoise and runs at 2000 feet/minute.


  1. Listen to the audio-recording of your “revised” teaching episode.
  2. In your notebook, write down the questions that you asked.
  3. Examine the questions you used while playing the role of teacher and write about what you learned about trying to use purposeful questions and eliciting student thinking.
  4. Read one of the messages from Smarter Than We Think. If your last name begins with A-M, read Message #14. If your last name begins with N-Z, read Message #16.
  5. Reflect back over all of the pedagogy discussions we have had in PMI and start a list in your notebook titled “Things I can do to help my students persevere when solving rich math problems.” Add at least three things to your list.

BTW: The “Messages” we’ve been reading come from the excellent book pictured below.




Day 2 of Functions & Algebra (7/26/16)

We began by reviewing last night’s math homework using the “Jigsaw” strategy.

Then we moved on in our Functions and Algebra notes, and we learned about Dan Meyer’s 3-act problems.  We looked at what makes proportional relationships special, and then pushed ourselves to solve problems based on proportions.

After lunch we discussed our responses to last night’s readings from Principles to Actions about questioning and eliciting student thinking. We used the reading to analyze the questioning practices of an 8th grade teacher leading students in the “Water Tank Task.” We both watched a video of her teaching and read a transcript episode.

We started our discussion of unit FA-3: Linear Relationships, but did not get past the first problem on currency conversion.  We will pick up there Wednesday morning.

Math Homework:

  1.  Create a “sequel” to one of the problems (1-5) on page FA2.12 that pushes the solver to use a systematic or efficient strategy to solve it.
  2. Revisit the milk problem on page FA2.12.

Pedagogy Homework:

  1. Look through your curriculum materials and identify a lesson that you might teach in the first few weeks of school. Refer to the picture below as a reference to find two “traditional problems” and rephrase them to make them “rich problems.” (Figure is from “Putting the Practices into Action” by O’Connell & SanGiovanni, published in 2013 by Heinemann).
  2. Also look through your curriculum materials and identify at least one lesson or topic that you teach that helps students build “floating capacity” for an idea we’ve discussed in the “Functions and Algebra” course.
  3. Read the “Upside-down teaching” article and think about how this connects to some of the time constraints we’ve discussed in class.