Kirkbride Elementary

Educators at Kirkbride provide daily experiences for learners to develop strong, foundational number sense that students will use throughout their lives. Students who have number sense have computational fluency in addition, subtraction, multiplication, and division of whole numbers. Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.

Fluency is a necessary skill in everyday life. For example, mathematical fluency is useful for:

• using mental math to decide the best value while shopping at a grocery store
• estimating a percent when determining a tip 
• being able to efficiently solve challenging multistep mathematical problems

Our student’s learning goal:

In Mathematics, students can communicate AND connect and reflect on their mental math strategies for addition to 100. 

NOTE:  Mental math involves looking at numbers and knowing how to manipulate them in order to make an equation easier to solve.

All teachers, across all grades provide students with learning opportunities aimed at increasing the numeracy success rates of our learners. To identify overall strengths and areas of growth, we tracked a cohort of learners, including two Grades Two classes. This cohort included a diverse range of learners that are representative of our school's population. 

What did this look like for the cohorts?

Communicating Mental Math Strategies

Each cohort class of students focused on communicating mental math strategies by engaging in Number Talks three to four times a week. A Number Talk is a short, on-going daily routine that provides students with meaningful practice with computation. Teachers intentionally selected problems for students to solve. During number talks, students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally. Our goal is not to necessarily “teach” the strategies, but rather to foster an environment where students can construct their own understanding. We are careful that we don’t teach the strategies as pieces of information to memorize; instead, we want students to be able to think flexibly when solving problems.

The practice of Number Talks was new to most of our staff.  Staff were introduced to number talks in our Number Routine Book Club.  Nine teachers at our school are reading Jessica Shumway's Number Routines books. They are Number Routines: Building Mathematical Understanding Every Day in Grades 3 -5 and Number Sense Routines: Building Numerical Literacy Everyday in K - 3. These teachers are trying "new to them" number routines to support the development of number sense. 

Additionally, our cohort teachers delved more specifically into Number Talks using Sherry Parrish's book Number Talks  to guide their practice. 

In the image below you can see one of our cohort classes engaged in a number talk.

 Our educator's created safe learning spaces for students to engage in communicating mathematical thinking. Teachers ensure that they provide significant wait time after posing a question and many of our staff request that students use "secret signals" to communicate with them. By using silent signals (e.g., placing their hands at their chests), teachers hope to decrease potential anxiety that can occur when students see that other's have an answer and they are still thinking. 

Connecting and Reflecting on mental math strategies

All our students are provided opportunities to reflect upon their mathematical thinking. When students engage in math experiences that include time to reflect on their reasoning and the thinking of others they are more likely to become self-reflective. They become better at thinking and making connections to other mathematical concepts and contexts. 

The teachers of our two cohort classes specifically use "Talk Moves" to help them facilitate reflective conversations.

Through these reflective discussions, the cohort teachers provide opportunities for students to:

• Clarify their thinking
• Investigate and apply mathematical relationships
• Build a repertoire of efficient strategies
• Make decisions about choosing efficient strategies for specific problems
• Consider and test other strategies 

Evidence of our students’ learning demonstrates that our Numeracy focus positively impacted our cohorts of learners. When surveyed and asked to communicate their students’ progress using the provincial assessment scale, teachers from both classes indicated that the majority of students demonstrated growth in relation to our numeracy goal. Teachers based their assessments on a triangulation of evidence, including anecdotal comments taken during whole class Number Talks, digital recordings of students sharing their thinking aloud, written work, and student self-assessment of their understanding of addition strategies.

What does this information tell us?

Growth was demonstrated in our March to June results. We saw a decrease in the percentage of students who are Emerging (-4%) and a large decrease in those who are Developing (-36%). Similarly, we saw a large increase in the percentage of students who are Proficient (+37%) and an increase in those who are Extending (+3%).  

Communicating:

Students demonstrated and identified multiple addition strategies. Our learners experienced success using strategies that made sense for the problem posed and that were efficient, accurate, and demonstrated flexibility with numbers.  Below are some of the mental math addition strategies the students developed. Each class created an anchor chart. 

Students also analyzed and sorted different computations by strategies.

Student:

 I can add big numbers in my head.

Teacher: How do you know how to add the numbers?

Student:

 I look at the numbers and then I think about it. 

Students communicate mental math strategies orally.

The majority of students quickly developed confidence sharing their mathematical thinking aloud during a Number Talk. Over time, students began to use mathematical vocabulary, such as the "one's digit, in the ten's digit, partners for ten, doubles, near doubles". By using math vocabulary, students were able to clearly articulate their thinking, such that their peers could understand and make connections. 

Below are two examples of Grade Two students from the cohort classes communicating their mathematical thinking, sharing the addition strategies they used when they computed mentally. 

Students communicated their thinking using pictures, numbers and symbols.

It took time and practice for students to develop their abilities to represent their mathematical thinking symbolically, using numbers and symbols. Most students achieved success by June, but for some students, this will be an area of continued focus. 

Reflecting and Connecting:

As students learned different strategies during the daily Number Talks, they self-reflected on their understanding. Holding up their hand, they used fingers to represent whether they had a solid understanding (five fingers) or they were developing an understand (three fingers) or were unsure of the strategies (a fist).

Students reflected on the strategies they were using. 

In class discussions, students were asked to reflect on the strategy they used and determine whether it was EFFICIENT, ACCURATE, and FLEXIBLE. 

Students made connections between strategies.

During daily Number Talks, students were provided opportunities to analyze strategies and make connections between strategies that were similar or different.  

Teacher: How are these strategies similar or different? 

Student: 

Give and Take is basically the same as Making a Friendly Number because you take a some to make the number a nicer number to add with.

Teacher: Tell me more...

Student:

When you take some from a number to give to another, you do that to make it a nicer number. Like with 18 + 6. I would take 2 from 6 to make 18 a nice, round number. It makes 20 and 20 and 6 is easy to add.

Moving Forward

Based on evidence of students’ progress in relation to learning goals, our next steps include:

• Increasing opportunities for groups of ELL students to work with the teacher using concrete materials to develop an understanding of strategies.
• Beginning in September. Start with one addition strategy and focus on this for several weeks prior to moving on to another.  
• Providing time for students to learn how to represent their mental math strategies using numbers and symbols. After students have become familiar with a particular addition strategy, provide students individual whiteboards, dry-erase markers, and erasers and ask them to represent their or a classmate's strategy on whiteboards. Using whiteboards is intentional, as they can easily be erased and hopefully will foster risk-taking.
• Continuing our book club with staff members, using Jessica Shumway's Number Routines books, as well as provide time for cohort teachers to model and collaborate with other staff members who want to initiate Number Talks in their classrooms.