Numeracy skills are fundamentally important to performing everyday tasks. Tasks such as thinking about if you have enough time to walk to school or figuring out which bike is the best value, require numeracy skills. At Strawberry Hill Elementary School our students are learning to think critically about the world around them, use reasoning skills to think logically about a situation, make sense of information, understand patterns, and make choices. These skills extend beyond the math classroom and can be used to solve problems and make decisions in a variety of situations, including real life scenarios.
Across all grades our learners develop, demonstrate, and apply mathematics understanding through play, inquiry, and problem solving.
The teacher read the story I’m the Biggest Thing in the Ocean by Kevin Sherry. The students use non-standard measurement (cubes) to measure ocean animals.
Students are working on developing their financial literacy skills. They are using concrete materials and pictures. They are looking at various ways to create $1 in collaboration with a partner. This allows them to demonstrate their mathematical thinking through play, inquiry and problem solving, while developing mental math strategies and making sense of quantities.
Estimating is an important skill and we want students to be able to determine the reasonableness of their answer. In real life students need to be able to use mental math quickly to arrive at a reasonable ballpark solution. Below is an example of estimation instruction.
In conversation with a partner, students are learning to make estimations using reason and comparison of known information. Students are using multiple strategies to estimate how many noodles are in a jar. Conversations with their peers encourage students to reflect on their mathematical thinking and help them to recognize we are ALL mathematicians!
Students use a 100’s chart to determine how many noodles are in a vase. They were shown what 10 noodles look like to help them estimate.
The student is using a number line and visual representations to demonstrate her understanding of fractions.
Every day at Strawberry Hill our team of educators provide a variety of educational experiences that prepare our learners for a world in which they think creatively and critically and communicate skillfully. Our students are learning how to reason, use logic, analyze, and persevere with problem solving in our math classes. These skills are needed for mathematics and real world 21st century skills that learners need regardless of what they do in their lives.
Our students’ learning goal is to:
All teachers, across all grades provide students with learning opportunities aimed at increasing mathematical thinking. To highlight and determine overall successes and gaps, we monitored the progress of a small cohort of students across intermediate classes (grades 5, 6, 7).
In our cohort, the first step involved researching which model of instruction worked best to improve and promote mathematical thinking, student engagement and perseverance. New instructional strategies were implemented.
Each math lesson was structured into three parts, which allowed students to think more and listen less. Mathematical routines were incorporated into lessons daily. These routines are quick, warmup activities that allow students to practice reasoning, demonstrate their prior knowledge, and engage in open-ended questions with many possible answers. This first part of the lesson was used to grab the students’ attention by presenting an engaging problem that helped the students get ready for the main problem.
Below is an example of a mathematical routine on fractions. Students were presented with the picture below and asked to describe the colours of the rectangle as a fraction and ratio.
The next part of the lesson is where students are presented with a problem. They often work with other students to figure out a real-world problem related to curricular content.
The last part of the lesson had students sharing their work and teachers using this time to ensure students understand the concept by asking prompting questions.
Students are explaining how they came up with their answers to the questions.
Evidence of our students learning demonstrates that our focus on improving the use of mathematical thinking skills has positively impacted our cohort of intermediate classes. Our teachers tracked the progress of their students’ math learning goal:
Growth was demonstrated in our January to June results. For our numeracy goal, we saw a decrease in the percentage of students who are Emerging (-10%) and a decrease in those who are Developing (-15%). Similarly, we saw an increase in the percentage of students who are Proficient (+10%) and an increase in those who are Extending (+15%). More descriptive evidence of learning that is specific to our numeracy goal is highlighted below.
The majority of our learners are able to explain their thinking and demonstrate how they completed the problem given. They are using relevant information from the problem, provide concrete and pictorial examples and use strategies and persistence to solve problems with their peers. In our cohort, all students experienced some level of success. Sixty percent of the students are now proficient in their ability to use reasoning and logic to help them solve math problems in class – compared to 40% who demonstrated proficiency earlier in the year.
An example of this success was a student who started the year lacking confidence in her math ability. In fact, she would often groan when math lessons started. At the beginning of year this student was at the emerging level in her ability to demonstrate her mathematical thinking when solving problems. She often did not know where to start and was not able to explain how she answered the questions the way she did. She often gave up when working on problems on her own.
When her teacher introduced mathematical concepts using the three-part lesson structure, a light turned on for this student. She found that working in groups and seeing how others were thinking helped her learn how to explain her mathematical thinking. She realized that there was not only one way to solve problems. This student is a visual learner and when the teacher incorporated visual representations and concrete materials, she was able to understand the concepts.
She said, “I found math problems that were projected on the board with visuals helped me think mathematically. I also found that when I had to create my own math problems and think in reverse, it helped me gain a deeper understanding. I also liked how we were asked questions randomly and placed in random groups.”
This student showed continued growth over the year, and she demonstrated an overall improvement in her ability to use reasoning and logic to solve problems. She has moved from emerging to developing and she has become increasingly confident in her ability and has taken on a more prominent role in class discussions. We are excited to see this student’s continued.
Students were tasked with placing fractions on a clothesline ordered from least to greatest. They used visual representations to solve the problem and explain their reasoning of why they placed the fractions where they did on the number line.
Students are using mathematical vocabulary to discuss angle measurement. They applied their knowledge of angles to create 2-D robots. They needed to have acute, obtuse, 90 degree and straight angles represented in their robot design. Students are communicating understanding of the concept pictorially.
This work sample below demonstrates the student’s ability to use his prior knowledge to help him use reason to make a logical estimation about how big an angle is.
Students are explaining their understanding of how to multiply numbers with decimals.
A student is able to use logic to recognize that the problem did not have enough information for them to solve the question.
After seeing the growth our students have made with their mathematical thinking skills, we will continue to use three-part lessons to teach mathematical concepts. Learning is social and we have learned that allowing discussion with peers has promoted thinking and the sharing of math vocabulary in our classrooms. Our learners are attempting and persevering with math problems more on their own and waiting less for the teacher to support their thinking. Time is required for students to dive into solving problems with peers and on their own and we will continue to provide that time.
Moving forward, we are going to expand this work beyond the cohort. This will require us to mirror the process and strategies implemented. We will start with using mathematical routines daily.