5.+Where+We+Are+Now

= Superior Greenstone District School Board = = Student Work Study Initiative = = Learning Supposition for 2012-2013 =

Written by Kathleen Schram
= Where We Are Now =
 * ** Student work is being used to drive instruction more **

//**Grade 3/4 School C**//



Rewriting words as they are hard to read:

Some strategies we can use?
 * Drawing (putting in number) and counting all
 * Repeated Addition
 * Skip Counting
 * Array (equal rows and columns)

Introducing multiplication - pushing students from direct representation to use of numbers (instead of 6 dots using the numbers 5 + 1) and how the 6 dots can be arranged into equal rows and columns....then naming the strategies so that students can begin to identify and use the language.

//**Grade 2/3/4 School A**//



Student representing parts in array, but not as equal rows and columns - Using the work for small group instruction to arrive at an understanding of how the different representations can be used to help us when multiplying - and building an understanding of an array as equal rows and columns.....

(Student work examples circled in the brown and blue and teacher instruction in red below)


 * ** Questions are being used as a form of feedback to help students to think more and better understand the relationships. **



Prompt on top sticky: "Could counting by tens and fives have help you to solve this question? How?"

Prompt on bottom sticky: "Did you really need to do all these steps?"


 * ** Conferences with students happening to push them to model their thinking using a different strategy **(changes made during conference done in green marker).


 * ** Anchor Charts in Classrooms are beginning to develop strategy walls and show relationships **

//**Grade 5/6 School C**//






 * ** Students are recognizing and naming the strategies they are using **




 * ** Math is being talked about more - teachers are co-planning and reflecting and comfort levels are increasing ** (examples from emails below)

"Hey Kath, having my students label which model/strategy they used on yesterday's multiplication question and wanted to make sure I have the right understanding. Is an algorithm a strategy using place value? And aside from a table, array, and number line can you think of other models used to show our thinking when multiplying?"

" Hi Kath, So I pulled up a place value chart on the smartboard and we talked about the numbers in the chart - which numbers they were and how we know. We talked about there only being the single digit in each column. I thought most seemed to understand - apparently not! I sent you some pics of what we did next. We wrote o-9 on wipeboard to understand where single digit falls and why. They I posed the question where does 10 go? I believe I sent you a pic of Jay's, He actually knew it was 1 ten but didn't add 0 in ones column. I tried again with 20-30 and sent a few pics of this. Obviously most still don't understand. Let me know what you think."

"... when I found out I was going to be teaching grade 8 math I was terrified. However, through planning with Kathleen, attending math camp, and having her visit my classroom on numerous occasions I along with my students grew more confident in my mathematical ability. Kathleen helped me put together diagnostic assessments for almost each unit and then we assessed them and decided where to go."

"Working with Kathleen was great! She was always open to listen to my concerns about students and to provide suggestions in a collaborative manner. She was truly focused on student thinking. Kathleen was a great resource for finding ways to model students' thinking in a variety of ways and to help students to become more efficient in their math work. Together we developed lesson ideas, math games to build capacity, and feedback for students. I highly recommend to all teachers working with a SWST in your classroom!"


 * So even though it wasn't a specific group of students followed throughout the year to create this supposition, growth around understanding the need for students to utilize a variety of math strategies and models was definitely developed. As teachers continue to model with math to develop number sense all year long - through an understanding of multiple representations; students will progress from that surface understanding (laden with misconceptions) to a deeper understanding - making meaning of what they are doing..... **

Continue on to 'More Supporting Research'