"Making Sense and Persisting Workshop" By Deborah Schifter

We were invited to attend a "Making Sense and Persisting Workshop" by Deborah Schifter.  This mathematics workshop using video studies of Grade two and Grade four students demonstrated students making sense of mathematical problems with which they persisted to find solutions and discussed their reasoning and how they engaged with mathematics.

Deborah is a principal research scientist at the Education Development Centre in Waltham, Massachusetts.  Her main interest at present is investigating algebraic thinking at the elementary level.  With other researchers (Virginia Bastable and Susan Jo Russell), she has been studying students ability to reason and notice how they can use their knowledge to solve a mathematical problem and to explain their thinking to others.  She has studied  "a student's ability to notice, articulate, prove, and apply generalisations about the behaviour of the operations."  A sequence of lessons for students in Grade 2 to Grade 5 has been developed and published in their book titled "But Why Does It Work? Mathematical Argument in the Elementary Grades".  (Heinemann 2017).

The book focuses not only on the mathematical content of the lessons, but also on what effective teachers need to know pedagogically to make these lessons worthwhile.  It is not enough to only know and use the content or curriculum.  There is a whole classroom culture that needs to be embraced for successful outcomes.

There are 8 common core standards.  These are
"1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning."

Students need to find "an entry point" where they can begin to work on a problem and to think how or what they can use to come up with a solution.  In junior classes they may use concrete materials or draw pictures to represent their thinking while older more mathematically proficient student might count on.  Asking questions that help them get started and continuing to ask "Does this make sense?" will make the student consider simpler ways to solve the problem.

Once a solution has been reached other options can then be looked at, answers check and analysed using models, pictures, mathematical equations and descriptions.  Younger children might use concrete objects and move these objects while they describe the actions they preformed to come up with a solution.

"Mathematically proficient students can listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.  They can communicate their arguments, compare them to others, and reconsider their own arguments in response to the critiques of others."

While viewing the videos and listening to the discussion I was thinking about the DMiC lessons we had been attempting and how we are learning the "teacher talk" to encourage the children in their thinking.  The children in the videos were of course much older than Year One but the level of teacher talk to get the children to reason and think without actually saying "you need to do...." was enlightening.  The open questions such as "Could we say that?"  gets children to critically look at their thinking.  "What are people thinking..." and " "How did other problems help you..." helped the children justify and explain their arguments.

We are just beginning our journey but when you see children working collaboratively to solve problems and to be able to say "I not not convinced."  and "That's the part I'm not sure." to a group of peers and with further discussion be finally able to say "Oh now I see it cause..." makes a pretty convincing argument that this style of mathematics makes children far more engaged in the process of making sense of mathematics and working through to find a solution.  We have a way to go yet but are taking our first tentative steps.

Thanks to Jodie Hunter for organising this event and Koru School for hosting it.