Differentiation in the senior mathematics classroomRachael Ouwejan

One Size Does Not Fit All

What is the issue?Differentiation:

“the strategic approach to curriculum design and instruction that builds meaningfully and responsively on students’ developmental needs and learning strengths”

(Crawford, 2008, pg 25). In an educational context, “one size

doesn’t fit all” (Gregory & Chapman, 2007, pg 1).

How to differentiate?1. Instruction is concept focused and principle driven... to

provide varied learning options. All students have the opportunity to explore meaningful ideas through a variety of avenues and approaches.

2. On-going assessment of student readiness and growth are built into the curriculum...

3. Flexible grouping is consistently used. In a differentiated class, students work in many patterns. Sometimes they work alone, sometimes in pairs, sometimes in groups... whole-group instruction may also be used for introducing new ideas, when planning, and for sharing learning outcomes...

4. Students are active explorers. Teachers guide the exploration. Because varied activities often occur simultaneously in a differentiated classroom, the teacher works more as a guide or facilitator of learning than as a dispenser of information.

(Tomlinson, 1995)

Tomlinson (1995) notes that tasks can be varied along a range of continua:

Concrete to abstract. Simple to complex. Basic to transformational. Fewer facets to multi-facets. Smaller leaps to greater leaps. More structured to more open. Less independence to greater

independence. Quicker to slower.

Key Questions? One of my goals for TE2 was to use differentiation in the

classroom, specifically in mathematics.

Therefore my topic for action research was “does my use of differentiation techniques in the mathematics classroom create opportunities to improve student achievement?”

I originally wished to explore the use of heterogeneous groups versus homogeneous groups in cooperative learning activities, but I had junior classes in mind when I posed this question, and did not teach any junior mathematics classes on this TE.

However, a secondary question I was able to explore was “are low and high achievers equally supported by the use of ‘streaming’ or instruction to homogeneous groups?”

What did I do? On my TE I compared the level of engagement and

achievement of students in a Year 12 (Level 2 NCEA) Mathematics class, considering whole class instruction and in a situation where we split the class into two groups on the basis of previously demonstrated ability in the unit of work.

I compared the achievement of the students in three ways: by observing the students in class, by discussing the effectiveness of the sessions with the students qualitatively, and summative assessment of the learning both via an informal practice test in class and more formally through the school-wide practice examinations.

  I also researched the topic through papers and

textbooks (see references).

What did I find out? I found that student achievement is supported by

using differentiation techniques in class. It was clear when observing the class and in

discussion with students that when instruction was pitched at one level students at either end of the spectrum were switching off and not participating in class activities (either “but I understand it already miss” or “why should I bother, this is going way over my head”).

Differentiation is cited by a multitude of authors as arguably the best way of supporting student achievement; for example, Carol Ann Tomlinson’s work (eg Tomlinson, 1995) or Gregory & Chapman (2007).

Secondary findings It was interesting to note that in practice, the degree of

improvement shown between the in-class practice test and the formal school examinations was markedly higher for the group of students identified as lower ability than for the high achievers. In fact, the high achievers as a whole performed much the same in the formal school examinations (and in a couple of instances, worse) as they had in the class test, whereas approximately half of the low achievers moved from a “Not Achieved” to an “Achieved” level.

It’s possible the students were motivated to study by their poor performance in the class test and therefore would have improved anyway.

However, my Associate Teacher and I swapped around the groups so it was not a simple matter of the students being affected by different teaching, and the degree of engagement with the material noticeably increased once the students were placed in the streamed groups.

Homogeneous grouping It is noted by Marcus (2009) that any group of

students will be heterogeneous by some measure, whether that measure is relevant to the learning activity or not (pg 2).

He also points out that in order to form either heterogeneous or homogeneous groupings, the teacher must have a good grasp of the abilities of the students involved.

It is clear to me from dealing with the students in my TE class that this information must be gathered in a variety of methods, relying not only on in-class observation or test results, as good performance in one area does not necessarily mean good performance in the other.

How does this inform my professional practice?This inquiry has shown me the importance of

delivering material at a variety of levels so it is accessible to all students.

This does not necessarily always mean streaming the mathematics class, but incorporating the principles of differentiation, specifically offering a range of learning activities and flexibility in how the classroom operates.

In mathematics this is most obvious in terms of: ◦ the speed of moving from concrete to abstract thinking; ◦ making smaller leaps compared to greater leaps (or the

size of the step when scaffolding); and◦ the degree of independence given to the students in

their working.

ReferencesCrawford, G.B. (2008). Differentiation and adolescent

development. Differentiation for the Adolescent Learner, pp 25-42. Corwin Press, Thousand Oaks, California.

 Gregory, G.H. & Chapman, C. (2007). Differentiated Instructional

Strategies: One Size Doesn’t Fit All. Corwin Press, Thousand Oaks, California.

 Marcus, R. (2009). Observations on Cooperative Learning Group

Assignments. Retrieved from http://www.thatmarcusfamily.org/philosophy/Papers/groupings.pdf, October 15, 2009.

 Tomlinson, C.A. (1995). Differentiating Instruction For Advanced

Learners In the Mixed-Ability Middle School Classroom, ERIC EC Digest #E536, October 1995. Retrieved from http://www.kidsource.com/kidsource/content/diff_instruction.html, 19 March 2009.