James Ardiel Elementary 23-24

Educators at James Ardiel provide daily experiences for learners to develop strong, foundational number sense that students will use throughout their lives. Students who have number sense understand number concepts. Number concepts in elementary school include foundational mathematical ideas about understanding and working with numbers. These concepts form the basis for more complex mathematical operations later on. Some key number concepts taught in elementary school include: 

1. Counting: Learning to count objects sequentially, understanding the concept of one-to-one correspondence, and recognizing numerals. 
2. Number Recognition: Identifying and naming numbers, both numerically (1, 2, 3, etc.) and in written form (one, two, three, etc.). 
3. Number Comparison: Understanding concepts like greater than, less than, and equal to, and using symbols (<, >, =) to compare numbers. 
4. Place Value: Understanding that the position of a digit in a number determines its value (e.g., in the number 24, the 2 represents two tens and the 4 represents four ones). 
5. Basic Operations: Introducing addition, subtraction, multiplication, and division concepts in simple contexts, often using manipulatives or visual aids. 
6. Number Patterns: Recognizing and extending simple number patterns (e.g., 2, 4, 6, 8, ..., or 5, 10, 15, 20, ...). 
7. Number Composition and Decomposition: Breaking numbers into smaller parts (decomposition) and combining smaller parts to form larger numbers (composition). 
8. Ordinal Numbers: Understanding the concept of ordinal numbers (first, second, third, etc.) and using them to describe the order of objects or events. 
9. Fractions and Decimals: Introduction to basic fractions and decimals, often in the form of halves, thirds, quarters, and simple decimal fractions like tenths and hundredths.

Our student’s learning goal:

In Mathematics, students can communicate and represent their understanding of Number Concepts. 

NOTE: Kindergarten to 10, Grade One to 20, Grade Two to 100, Grade Three to 1000, Grade 4 to 10 000, Grade 5 to 100 000, and on to include millions, decimals, fractions, and percentages.

All teachers across all grades provide students with learning opportunities to increase our learners' numeracy success rates. We tracked a cohort of learners, including 13 classes from Grades Kindergarten to Grade 7, to identify overall strengths and growth areas. This cohort included a diverse range of learners representing our school's population. 

What did this look like for the cohorts?

Communicating and Representing

The cohort class of students focused on communicating and representing their understanding of number concepts in different ways.  Nine classes used "Counting Collections" as their weekly instructional strategy to increase their students' understanding of number concepts. Counting collections is a research-supported instructional strategy commonly used in mathematics education. It involves providing students with a collection of objects, such as buttons, coins, or beads, and asking them to count the items in the collection. However, counting collections goes beyond simple counting; it encompasses a range of mathematical concepts and skills.

The practice of Counting Collections was new to most of our staff.  Staff were introduced to Counting Collections through a "Lunch and Learn" in the fall of 2023.  These teachers were provided with the book "Choral Counting and Counting Collections: Transforming the Pre-K - 5 Math Classroom" by  Megan L Franke and Elham Kazemi. 

 Four classes used "Hands-On Math Investigations", sometimes called Numeracy Centres, three to four times a week to increase their students' understanding of number concepts.  Hands-on Math Investigations are mathematical activities designed for individuals, partners, and/or small groups of students. These activities are inviting and engaging and assist students in developing mathematical understanding. Students need daily opportunities to engage with mathematical ideas purposefully and playfully. They provide time for authentic, independent practice that connects to their learning through whole-class quality instruction.

STUDENT:

Math is my favourite subject!

TEACHER: Can you tell me more?

It is just so fun. The things we use are the best - like sequins and frog erasers. Sometimes I also play games with a friend. 

Counting Collections and  Hands-On Math Investigations deepen students' understanding of number concepts and foster a positive attitude toward mathematics by making learning interactive and enjoyable.

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 most students demonstrated growth in relation to our numeracy goal. Teachers based their assessments on a triangulation of evidence, including anecdotal comments taken during Math Investigations and Counting Collections lessons, digital recordings of students sharing their thinking aloud, written work, and student self-assessments of their understanding of number concepts.

What does this information tell us?

Growth was demonstrated over the year. We saw a decrease in the percentage of students who are Emerging (-19%) and another decrease in those who are Developing (-20%). Similarly, we saw a large increase in the percentage of students who are Proficient (+33%) and an increase in those who are Extending (+6%).  

Communicating and Representing:

Students communicated and represented their understanding of number concepts in many ways, including orally, concretely, pictorially, and symbolically. Teachers observed that students were better able to demonstrate their learning with concrete materials and that using these materials increased students understanding of number concepts, making them better able to shift to symbolic representation.

Growth over time:

In October, our early primary classes took these initial Counting Collections images. Initially, as shown in the left picture below, many students could count objects and state how many were in the collection but required the assistance of a number line to help them identify the corresponding numeral.  This also supported students with one-to-one correspondence. Over time and with growth, as evidenced in the photo on the right, students could count and identify numerals independently.  

As students were offered larger quantities to count, some students initially struggled with understanding the place and value of digits, as evidenced in the photo on the left with the numeral reversals. Teachers provided support, such as 100 charts and tens frame organizers, to assist students' place value learning.

Students' repeated experiences with Counting Collections increased their ability to represent number concepts in multiple ways. In the examples below, a Grade Three student communicates his understanding concretely using materials, pictorially and symbolically.

It was also exciting to observe the increasing complexity of students' ability to represent their learning across the intermediate grades symbolically.

Moving Forward

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

• Increasing opportunities for ELL students to use their first language is important as it provides entry points for them and continued access to learning. 

• Intermediate teachers realized the value of offering hands-on materials to increase engagement and motivation and assist students in developing understanding in a way that using concrete materials provides.

Teachers shared:

I am amazed at how using concrete items assisted the students in developing a depth of understanding of concepts that often struggle with, such as equivalent fractions. By using materials, they could really see the fractions and make sense of the learning. 

• Teachers also found that conferring with students allowed them to take notes about what students could do. This descriptive assessment provided valuable information for future lessons. 

Sample Anecdotal comment: Students demonstrated their ability to skip count by 2's to 40. Moving beyond 40 they struggled and started to guess. Next lesson, pull students in small groups to assist them in seeing the hundreds chart as a helpful tool they can use to assist them in skip counting by 2's beyond 40.