Tag: frayer model

Just got back from Chicago, and have so many thoughts rolling around in my head!! Blog ideas about navigating the conference, Ron Clark, Doris Kearns Goodwin (this is my new role model – her storytelling, her presence, her speaking ability and intelligence are all qualities I aspire to), presenting do’s and don’ts, and writing ideas are all swirling around in my head. So, in trying to stay focused, I’m starting with my big passion – communicating mathematically.

There were few workshop options in the math writing/communicating world, and the first one I went to was titled Elevating ELL Discourse in the Mathematics Classroom, presented by Sherry Ayala and Sylvia Olmos. Although the title didn’t reference writing, the summary did. Much of this workshop turned out to be similar to work we have done in our district around the 5 Practices. Lately as I’ve attended workshops, I’ve noticed quite a bit of similar learning, which leads me to look for the “nuggets”, or the new piece of learning that I can attach to prior knowledge. In this case, my nugget was how we teach and practice math vocabulary.

Students partner up, and explain their thinking around a problem, such as 324 – 165. As a teacher, you’ve considered what vocabulary they may use around this problem, such as subtract, add, ones, tens, hundreds, regroup. You provide the students with a small table, so that the listening partner can tally the number of times the partner used the vocabulary words.

subtract	Tally:
add	Tally:
ones	Tally:
tens	Tally:
hundreds	Tally:
regroup	Tally:
equal(s)	Tally:

From there, the listening partner can paraphrase back to the speaker what s/he said, and the speaker can self assess. Why didn’t I use regroup (or ones/tens/hundreds/etc). Did I need to? How could I explain differently so that I could use a different vocabulary word? I’m super curious to try this out in a classroom to see how students respond. The vocab words chosen are all based on what you have taught and what you expect them to use – being aware that the flexible thinkers you have molded will likely be able to find ways to explain that would change the vocab you are looking for.

The other workshop I went to was titled Strategies for Teaching Effective Mathematical Communication, from the book by the same name, presented by Laney Sammons and Donna Boucher. This one intrigued me because it was directly on mathematical writing, and I’m searching for different research based opinions and ideas to round out the work we have been doing so far. Again I saw many similar ideas to what we have already been doing with discourse (oral communication ideas, using CRA in math progressions). I noticed that this workshop also brought up the idea of developing math vocabulary, including the use of the Frayer model (along with a foldable that I’ve referenced in many of my own trainings).

Another nugget from this workshop was the inspiration to redo our criteria on our rubric. Their suggestion, based on work from the Ontario Ministry of Education, was to examine:

• Precision regarding details, strategies, observations, and calculations
• Explanations of assumptions and generalizations made
• Clarity in logical organization
• Cohesive arguments presented
• Elaborations that explain and justify mathematical ideas and strategies
• Appropriate use of mathematical terminology

I think that this list makes for a nice set of criteria beyond what we have used up to this point, and the work now will be to blend it with our current rubric:

So what is next for my math writing partner in crime and myself? We are looking at streamlining our presentation so that the focus is not the lessons that are prepared for classes, but instead an approach more linked to disciplinary literacy. An approach in which the vocabulary is introduced, clearly understood and practiced. One where there are multiple criteria for success and we can narrow lessons down to one or two of those criteria each time to develop, strengthen, and support their communication in writing. Plus, we need to go over the book, Strategies for Teaching Effective Mathematical Communication, to look for more ways to refine our thoughts and our rubrics.

The last nugget, that I should probably save for my navigating the conference post, is: Just because you didn’t attend the session doesn’t mean you can’t spy on the notes! So the Connecting Math and Literacy session by Alex Kajitani was at the same time as another session. In his presentation, he had this wonderful quote from Marilyn Burns. Besides wondering why I hadn’t seen it before, I was struck by the clarity it brought me.

Writing in math class isn’t meant to produce a product suitable for publication, but rather to provide a way for students to reflect on their own learning and to explore, extend, and cement their ideas about the mathematics they study.

Marilyn Burns
Educational Leadership, 2004

Spoiler alert – that one will be in our next presentation. Thanks to all who developed and presented at the conference! You challenged us to develop and refine our own thinking, and I am grateful for it.