By Sky Cressman & Michelle Lang (Waterloo Region DSB)

“It was like, I don’t speak English before, you know, and Mrs. Cressman she makes sure I understand. She explain to me to understand. Now this year, it’s very easy for me, the maths, you know, because last year she teach me so much.” 

Abdallah, a student in Sky Cressman’s 2018-2019 MAT1LZ class

What We Were Doing Just Wasn’t Working 

(Sky Cressman -secondary Math teacher)

I am fortunate to teach at a high school in Waterloo Region rich with diversity. The student body is made up of students from many different backgrounds and cultures, who naturally bring a range of varied first languages. We welcome and celebrate these differences at Eastwood Secondary School. And along with these differences, come very unique student learning needs. It is these needs that have given rise to a terrific literacy program aimed at early literacy development for our English language learners. 

Prior to 2017, however, our English Literacy Development (ELD) numeracy program hadn’t yet received the same attention. This was evident in the general lack of necessary resources (concrete math materials, adequate classrooms), as well as inconsistent teacher timetabling. Further, beyond the logistical aspects, the content and pedagogy that were shaping our program were simply unsuitable for our ELD population. We were using the essential-level, grade 9 Ontario math curriculum, even though ELD students have minimal to no formal instruction prior to their arrival. Sure, there was some focus on vocabulary and content-specific language, but the math curriculum itself was addressing content 6 to 8 grade levels beyond the students' understanding. The attempt to deliver this unsuitable curriculum meant that my teaching methodology focussed very much on procedures and algorithmic processes, rather than on foundational understanding. It became clear that students were following my processes but had very little understanding of the math concepts lying beneath. Our numeracy program at this time was failing these kids. We were sending them off without the fundamental math skills necessary for life beyond high school, never mind skills to continue on to higher education. This quickly became an equity issue for me. With the program as it stood, our ELD population did not have access to effective numeracy education that would allow them to further their knowledge and skills toward proficiency.

Our Context 

(Michelle - Math Learning Service Consultant)

In Waterloo Region District School Board (WRDSB) alone, we have approximately 350 secondary English language learners (ELLs) in the English Literacy Development (ELD) program. Although limited in their prior schooling and first language (L1) literacy, these students come to us with a wide variety of background experiences and learning strengths. In their first few years of high school, they will begin to develop English literacy skills in five language courses provided by the Ontario Ministry of Education: ELDA through ELDE1. However, despite a policy that states explicitly that students in ELD programs should receive “additional support...through an intensive program designed to accelerate the student’s acquisition of proficiency in everyday and academic English and the appropriate knowledge and skills of literacy and numeracy (p. 18, emphasis added)”, we have no Ministry-approved courses to specifically address the numeracy learning needs of our students in these programs. 

Reaching Critical Mass and Implementing Change

In 2017, the number of students enrolled in ELD math courses reached a critical mass and additional board resources were allocated to address the concerns that many of us were expressing. We made plans to gather data focused on the mathematical understandings our students were coming to us with. Through observations and conversations with students and teachers in the ELD math classrooms, we identified some student learning strengths and needs. Then, using PRIME Number and Operations Diagnostic Tools3, we completed 66 one-on-one interviews with students. This assessment data suggested that most students were within late phase 1 or early phase 2 on the PRIME Number and Operations continua, which is equivalent to about grade 1-2 in the Ontario curriculum. It was time for changes to both the content that teachers were teaching and the methods that they were using to address that content.

Changing My Pedagogy

(Sky)

By the 2017-2018 school year, we were lucky to have at Eastwood a very unique literacy program well underway for our ELD population. The focus was on small group instruction - guided reading and writing. Although a very different subject area, to observe such a program gave our ELD math teachers an opportunity to see how students who come to us with varied levels of math understanding might have their numeracy needs met all within the same classroom. By flexibly arranging students in small learning groups, according to ability and/or language, students could access material at suitable entry points, and continue to progress at a pace determined by their learning. My personal beliefs of what a secondary ELD math classroom should look like were challenged at this point. I could no longer go back to the teacher-centred, autocratic style of instruction, when I witnessed firsthand how effective the activity-based, small group model could be.

Our instruction model was only half of our concern, however. Our MAT1LZ course content was simply too advanced for our students. My son, in grade 3 at the time, brought his math homework home one evening. I realized that many of my students at the time would not have been able to do this primary-level math. And if that was the case, they would have no chance of applying concepts such as money, proportions and geometry to their environments - which really is my goal as a math educator. Yes, the elementary math curriculum is where we needed to begin. And so the back-mapping of our 1L curriculum to the early elementary curriculum began. 

With the plans for a big shift in our ELD math program, we recognized quickly that a school team approach would be best. Teachers, guidance counsellors, administrators and board consultants all played a role in carving out the logistics of this program. We considered things like fluid student timetabling to allow students to be moved mid-year between our levelled 1LZ and 2LZ classes. We also planned for the students to take math for the full year, rather than only one semester, to maximize their progress. This also required timetabling consideration. In line with scheduling, teachers of ELD math had to have suitable classrooms, with round tables, conducive to small-group learning. These classrooms would need an inventory of supplies and manipulatives, allowing students to discover math concepts and to illustrate their understanding in a concrete way. And finally, it was important to give thought to the human resources to be devoted to this program. Educational assistants and peer tutors have now been scheduled into our ELD math classrooms, to assist in the work we do within our learning groups.

Evidence that Small Group Instruction is Effective 

Over the past two years, we have implemented small group guided instruction in several of our secondary ELD math classes.

The success of this targeted model of instruction is evident in the students’ engagement with the math, their visual representations of the strategies they use, and their willingness and ability to explain their thinking. Small group guided instruction also allows the teacher to more accurately assess their students’ understanding of the math concepts.

“With the old model, I really didn’t know, at the end of the day, how far I had brought them because all students were getting the same material at the same level and I was trying to bring them up to this one single bar no matter where they were starting from. [After implementing small group instruction] this year, I knew what every kid could do in terms of the various concepts under the fraction umbrella, for example, or I knew what they could do with patterning or the operations. I knew exactly where they had started with each of those concepts and also where I had been able to bring them to. That was just really clear in the end, what specific learning expectations that they had met or that they were still in progress of learning and needed more time for next year.”

(Sky, during an interview with Michelle in June 2019)

Setting Up Small Group Instruction in Your Classroom

Small group guided instruction allows you, as the classroom teacher, to engage your students with the mathematics, track their individual progress, provide authentic and timely assessment, and plan for “just right next steps” to meet each of your students’ learning needs.

To set up small group instruction in your classroom:

• Identify your students’ areas of strength and need in numeracy through observations, conversations, and diagnostic assessment tasks. (We are using the Grade 3-4 Leaps and Bounds4 topic-specific diagnostic tools.)
• Organize your students into small groups of 3-4 students based on a similar identified numeracy learning need and/or common first language.
• Find or develop learning tasks that address the identified learning needs for each of your small groups. Include at least one learning task that students can complete individually or with a partner, but independent of you. (We are using a variety of sources for learning tasks, including Leaps and Bounds, MathUP5, and our board’s Sample Long-Range Plans for Mathematics, Grades 1-66.)
• Create a schedule for small group rotation, whereby one group is learning new content with you, the teacher; another group is reinforcing their learning, ideally with an EA or peer tutor; and one or two other groups are consolidating their learning through independent activities and/or games.
• Sample Small Group Guided Instruction Schedule:
• To help you to advocate for allocation of human resources (EA time, access to peer tutors) and of physical resources (concrete materials to support learning, furniture to enable small group instruction) to best support your students’ learning, enlist the support of a team of educators in your building, including your school administrator(s), guidance department head, ESL department head, and math department head, as well as board-level support staff.

Conclusion: Our Moral Imperative

Although we are continuing, every day, to learn more about the students we serve in our ELD math courses, what we have learned so far emphasizes for us the value of small group guided instruction for reaching and effectively teaching some of our most vulnerable learners. We have seen that through targeted, small group guided instruction, our students are engaging more deeply with the mathematics, representing their mathematical thinking using a variety of tools and strategies, and gaining competence and confidence in their understanding of mathematics. It is incumbent upon us, then, to embrace this method of teaching within all of our ELD math classes. 

The students in our ELD math programs are motivated to learn and aspire to contribute to their communities. Indeed, the Ontario Ministry of Education policy document for ESL and ELD programs mandates that, “In secondary schools, placement in a grade or in specific subjects will depend upon the student’s prior education, background in specific subject areas, and aspirations (p. 21, emphasis added).” 

“I want to study about international immigrations. I want to help people, like help refugees.” 

Deborah, a student in Sky’s 2018-2019 MAT1LZ class

“I want to study for engineer.” 

Abdallah, a student in Sky’s 2018-2019 MAT1LZ class

“I like to be fashion designer...I need math in the fashion design.” 

Emel, a student in Sky’s 2018-2019 MAT1LZ class

Let us respond to these students by teaching them mathematics in the ways that we know will best meet their needs as learners and as young people who want to make a difference.

End Notes:

• Queen's Printer for Ontario. (2007). Ontario curriculum: grade 9 to 12 - English as a Second Language and English Literacy Development. Toronto.
• The Ontario Ministry of Education. (2007). English language learners: ESL and ELD programs and services: policies and procedures for Ontario elementary and secondary schools, Kindergarten to Grade 12. Toronto.
• Small, M. (2005). Prime (professional resources and instruction for mathematics educators): number and operations strand kit. Toronto: Nelson Thomson.
• Small, M., Cubota-Zarivnij, K., Lin, A., & Borgen, K. (2011). Leaps and bounds toward math understanding 3-4. Toronto: Nelson.
• Small, M., & Duff, D. (2019). MathUP. Oakville: Rubicon.
• WRDSB (2018). Sample long-range mathematics plans, Grades 1-6.

Sky Cressman is a secondary school mathematics teacher with the Waterloo   Region District School Board. She has taught high school math since 2005,   recently adding ELD math to her professional portfolio. She believes that 

everyone is capable of learning math and pursuing higher level studies in the 

subject area, if they are met with a program that is appropriate in both 

curriculum content and instruction. Her personal goal is to have each of her 

students recognize that when these conditions are coupled with hard work and determination, there is no limit to what they can achieve. 

As a Learning Support Services Consultant with over 25 years of experience in the teaching and learning of mathematics, Michelle Lang advocates for and supports both teachers and students in ELD math programs within the Waterloo Region District School Board. She is passionate about ensuring that all students have equitable access to math content and instruction that meets not only their current learning needs, but also their goals for the future.