*There are a lot of elements that go into a balanced mathematics program. Beyond a deep understanding of modeled, shared, guided and independent mathematics, teachers need to have a clear understanding of: setting conditions for learning, building classroom community and the effective use of assessment.*

*It's completely fair to say that implementing an effective, balanced mathematics program is impossible without these foundational understandings. Perhaps in much of our sharing as educators, we gloss over some of the steps along the way, assuming that our colleagues and even leaders 'know what we mean' or are completely aware of the work that goes into effective programming. I open with this sentiment because I feel that anyone unfamiliar with the aforementioned concepts and practices should start their journey by exploring these building blocks.*

As we continue to work through this project, Katarina and I have deepened our understanding of how to effectively use assessment for learning to guide instruction. This isn't something new for Katarina, but the level of intentionality that this project asked for allowed her to refine her thinking. I had the pleasure of learning along with her, co-planning at times and providing an "outside looking in" perspective whenever needed.

While all of the parts slowly came together, Katarina continued to find it difficult to really get the guided portion of the program built into the classroom routine - we touched on that in our previous post. On April 24th we met to discuss what Katarina called her most effective and most comfortable implementation of guided practice so far:

"It all starts with an assessment for learning, a diagnostic, I did about eight weeks ago" Katarina started our discussion. "I found out that my students, as a whole class, really didn't know how to use place value to read numbers to the right of a decimal; they struggled with tenths and hundredths. The assessment for learning also helped me to find students who hadn't consolidated place value for whole numbers. I knew exactly where I wanted to start my whole group discussion".

Katarina explained to me that her whole group instruction aimed to help students understand 'how digits after the decimal work' with a special focus on the fact that decimals represents parts of a whole and, as such, are fractions. The class discussion branched further into how to read decimal numbers with place value (eg: saying five tenths when we see 0.5) and ended off with questions and discussion around recognizing when zero is used as a place holder versus when a zero is actually denoting a value (eg: 0.5 is the same as 0.50 BUT it's not the same as 0.05)

"My favorite part was all of the a-ha moments students were having around the connections between decimals and fractions!" Katarina explained to me.

Katarina formed groups using data from her assessment and observations she made as she circulated to conference and support groups of students as they worked collaboratively to respond to her prompts (we have a nice picture of Katarina's notes, but they include student names so we hope you'll take our word for it!).

"I found that I could make appropriate groupings because I know them; I thought about the depth of student responses, and what they demonstrated orally, not just what was being recorded on their pages. Conversations mattered when making my groups." Some other factors Katarina considered when making her groups included the leadership characteristics of group members and their individual work habits.

Katarina explained to me that the groupings she made were to be used during mathematics instruction over the next few days. She edited and scaffolded EQAO questions for three of her groups, she had guided instruction and conferencing with a fourth group while a fifth group worked on a number sense mission she had set up in Knowledgehook. Students would only be directed to Knowledgehook once they'd had a chance to participate in guided instruction as these missions were meant to check for student understanding (and could be used to further guide "circling back" in instruction).

Katarina summed up her learning to this point as we ended our chat: *“I have learned about different ways to approach teaching mathematics and I have been able to move my teaching through involvement in the project. I found ways to take the theories and concepts and apply them in ways that were effective for my students and for my teaching. I've also noticed that students have improved in the processes of reasoning and proving as well as communicating"* (we'll aim to be more specific about this quote in our next post!).

As a next step, and thanks to an idea I picked up at our most recent TLLP team meeting, I suggested that Katarina consider adding a 'today I learned' component to her mathematics instruction. The idea would be for students to use screencastify to record a response to the very open prompt: 'What did you learn today'. Student responses could be recorded in this manner on a rotating schedule, similar to the way guided instruction is set to work. These recordings could very easily be the content for a dedicated 'topic' in google classroom, but here I am getting ahead of myself, adding more to our "to implement" list!

As we come closer and closer to the end of our project we're developing a comfort with balanced mathematics that, admittedly, has been a long time coming. I've also found that our "to try" list continues to grow and is far longer than the school year will allow, which is probably exactly as it should be.

Thank you for sharing Emile! Very informative, and I took away from some of the inspired thoughts you had. It makes me 'think' about how I open up the forum of decimals and it's comparison to fractions. Having students 'understand' the decimal is very different from having them simply 'rote' learn a concept. I like your open dialogue, and am sure your students benefit from having your math expertise!

Yolanda