Our challenge:
Student Challenge: How do we accelerate achievement in maths when students have a range of maths abilities with various gaps in maths knowledge?
Teacher Challenge: How do we accelerate achievement in maths when teachers are tasked with teaching a classroom of students with a range of maths abilities and with various gaps in maths knowledge?
Personal justification of running an extension maths programme (see previous blog post):
A typical classroom includes a range of mathematics levels. How do we as teachers realistically support the children who find maths really challenging while also extending those who find the logic of maths more natural? It is challenging, that's for sure! We have a really unique opportunity here where we can run an extension programme for those children who we identify as gifted in Maths, allowing the classroom teachers to spend that session focussing on building the knowledge for the rest of the class. The extension group can then return to their classroom and use their new knowledge and skills to work alongside their other classmates to build their maths knowledge.
What does the Manaiakalani research say to provide evidence and justification for this inquiry?
See previous blog post
What does the wider research say?
In any inquiry, it is important to have tools, measures and approaches which are planned for use so we can get a more detailed and accurate profile of students' learning in relation to a challenge. If we aren't doing this, then any implementation of something new is really just a guess!
To start this off, I went to the research. Over the course of this inquiry, I want to make sure I look at multiple view points to see how to best teach extension level maths students.
Text: Linchevski, L & Kutscher, B. (1998). Tell Me With Whom You’re Learning, and I’ll Tell You How Much You’ve Learned: Mixed-Ability Versus Same-Ability Grouping in Mathematics, Journal for Research in Mathematics Education, Vol. 29, No. 5, P533-554.
Key Points:
- Ability Grouping (subject-by-subject, also known as tracking vs. all subjects at once, also known as streaming).
- Ability grouping can be used to change content, pace or teaching methods.
- Some research has shown that by ability grouping, the gap between abilities increases.
Personal note: does this mean it is negative effect for those who do better? We will be doing things differently where we will be reducing class numbers for an hour per week so the classroom teacher can give more time to those who need it for the basics of maths.
- Quality of oral language used (within communication) differs greatly between lower ability groups and higher ability groups. With this comes differences in expectations (Gamoran, 1993).
Personal note: we will need to make sure we don't allow this to happen.
- Preteaching (described in study on page 536). Mix of homogenous and heterogenous groups. Students have preteaching in homogenous groups. "Whenever a teacher felt that a large, specific homogeneous group of students
would benefit from the teacher’s direct intervention, that setting was used—for
example, to better prepare weaker students to be integrated into a planned heterogeneous group activity." Page 536.
Personal note: This sounds very similar to what we are trying to achieve.
- Homogenous (children of same ability) vs. Heterogenous (children of different ability) grouping
- Study 1: After 1 year, in 10/12 schools, Mixed ability grouping did not impact the gap between achievement between children of various abilities. In 2/12 schools, it widened the gap however there were signs of this gap reducing after two years.
- Study 2: Mixed ability grouping was hugely benficial to average to lower ability students. Higher ability students did not lose any achievement by being in mixed ability grouping.
- Goroman (1992) - workshop type pedagogy - look more into this.
- Overall, this Journal Article and studies are in favour of Heterogenous grouping/ Mixed Ability Grouping for teaching mathematics.
Next Articles to look into:
Gamoran, A. (1992). Is ability grouping equitable? Educational Leadership, 50 (2), 11–17.
Gamoran, A. (1993). Alternative uses of ability grouping in secondary schools: Can we bring high quality instruction to low-ability classes? American Journal of Education, 102, 1–22.
