We are happy to announce we will be offering the PMI workshops in July 2020.  These are the same workshops we have offered in past summers. The workshops will be July 20 to 31st.  Participation is free, with stipends ranging $800 to $1800 offered for Pennsylvania-based teachers to offset opportunity costs. More details and an application are available at the 2020 Workshops Page ..read more

Looks like it’s been a while since I updated here.  My semesters have been over-full. The good news is that we are doing a lot of good work to get ready for the 2020 Summer PMI workshops.  More will get posted here soon, but applications are already open ..read more

We began the day with some more work on linear and proportional relationships through the Purple Paint problems. Then we did Burning the Candle problems. We were especially interested in graphical representations of these scenarios and connected graphical representations to one another (red to blue; blue to red; total to red) and to other representations (tabular, symbolic, contextual). Then we discussed inverse relationships and we concluded by discussing at a “meta” level what things we might be interested in when describing “co-variation.” After lunch we followed a jigsaw arrangement to dis ..read more

Today we talked about unit rates (and representations thereof) based work with the Coffee Maker problem and the Perfect Pint of Pink Paint. See the image below. Then after lunch, we discussed the reading about “access and equity” from Principles to Actions. We discussed productive vs unproductive beliefs, we played with the scenario cards, and we connected all of that with the 5 strands of mathematical proficiency the Standards for Mathematical Practice The Effective Teaching Practices Then we solved the Hourglass problem, and compared student work thereon. Tonight you are invited to pre-read ..read more

This morning we spent learning about why the integer (positive and negative numbers) operations work! We talked about adding, subtracting, and multiplying signed numbers – ultimately learning why a negative number times a negative number is a positive number!!! We then embarked on solving the Kayak problem. After lunch, we continued with the Kayak problem before moving on to pedagogy. During the pedagogy time today, we read Cathy Seeley’s message titled “Upside Down Teaching” and talked about positive reactions to the message and challenges with teaching in this way. We then did the “Planning ..read more

In the morning, we welcomed new teachers and started thinking algebraically! We revisted Otto and Hannah (Sibling Rivalry: Unknown Quantities), but this time they were eating Halloween candy, comparing heights, and running! After lunch, we learned about performance and learning goals (Band Concert Task) and revisited how to use goals to support asking assessing/advancing questions (like we did last week with the Brownie Problem). We then did an activity where we analyzed a set of student work (Walking from School Task) and discussed how goals can support selecting, sequencing, and connecting s ..read more

This morning we: Discussed the “sum of odds” problem (1 + 3 + 5 + …….+ 99) Built on that to work on the “Insatiable Caterpillar” problem Then we worked on the Piggy Bank Problems Then we played (and nailed!) the name game After lunch we: Discussed how developing conceptual understanding can support procedural fluency. We generated the list below: ”Concrete to abstract” : concrete action supports conceptual understanding, and this provides access to be able to model themselves Hands-on activities –> mental representations –> supports abilities to do procedures If only procedural skills: k ..read more

Our math for the morning explored the theme that “the same quantities have many names, and context determines the most useful name.” We focused on discussions of the equal sign, place-value, and fractions and algorithms for computing operations of addition and subtraction. In the afternoon, Fran presented three frameworks that guide PMI’s design and implementation: Strands of Mathematical Proficiency: What does it mean to know mathematics? Here are the definitions of the Strands of Mathematical Proficiency that were in the PowerPoint today:Adding it Up: Helping Children Learn Mathematics, Nati ..read more

We had a great first day! We began with our first problem, the Star Spangled Banner Problem.  Participants shared a variety of solution methods using patterns found in numerical tables, patterns in the drawings of the stars, and also using functions. We did the Two Gross problems and discussed the adjective-noun theme, and then we did some fraction problems in which we “messed with the whole.” After lunch, we discussed “Smarter than We Think” (by Cathy Seeley). We developed a list of phrases to use instead of “You are smart” We watched 2 videos about Carol Dweck’s research on fixed vs. growt ..read more