We in New Zealand have a growing mathematics problem. We are not getting better, and by the best measures, getting worse. Poor mathematical performance correlates with limited life outcomes, so its important to get it right. While there are a range of reasons for the lacklustre performance, there is one that no one talks about yet is potentially a prime reason for our troubles.
We don't teach, or use, appropriate learning strategies. Literacy (reading, writing, speaking and listening) has a bootstrapping effect, this is less so in maths. Therefore, you might get away with poor strategies in literacy, but poor strategy use in maths is unforgiving.
There are three categories of learning strategies: Memorisation strategies, elaboration strategies, and control strategies.
Memorisation strategies are based on the idea that you want to be able to recall the relevant information when you need it. Sound reasonable? It shouldn't. This approach correlates not only with lower performance, but negative performance. Did you catch that? Negative performance.
Elaboration strategies are strategies designed to elaborate knowledge. Control strategies are related to organising and managing yourself. Both relate to high performance.
Memorisation strategies are passive, and therefore cognitively simple, resulting in little long-term cognitive change. In contrast, elaboration and control strategies result in cognitive complex activity that results in learning.
How does NZ perform in regard to the strategies we teach and use?
Last year the OECD issued a report that looked at the different strategies used and taught by different countries. Drawing on PISA results the authors found that the high-performing countries teach and use elaboration and control strategies, the lower-performing countries use memorisation. Guess where NZ sits? Unfortunately, nearer the bottom than the top.
Also note, that the researchers did not ask the teachers - who would argue that they do not rely on memorisation. Rather they asked the students. Student feedback reveals that they have not been taught to use elaboration or control strategies. Despite what teachers might suggest, the fact is that the students’ beliefs are oriented toward memorisation. Click the title of the paper to go directly to the paper.
Echazarra,A., et al. (2016), "How teachers teach and students learn: Successful strategies for school", OECD Education Working Papers, No. 130, OECD Publishing, Paris.
Fewer 15-year-olds in Hong Kong-China, Japan, Korea, Macao-China, Chinese Taipei and Viet Nam reported that they use memorisation as a learning strategy than did 15-year-olds in some of the English speaking countries to which they are often compared (Purdie and Hattie, 1996). For instance, 12% of students in Japan and 17% in Korea said they learn as much as they can by heart when they study for a mathematics test. By contrast, 26% of students in Canada, 28% in Ireland, 29% in the United States, 35% in Australia and New Zealand, and 37% in the United Kingdom reported so (Figure 4.1). This may sound surprising to many but mathematics instruction has changed considerably in many of these countries (OECD, 2011). Students in Ireland, the Netherlands, Spain, the United Kingdom and Uruguay reported the most frequent use of memorisation strategies, while those in Albania, Macao-China, the Russian Federation, Serbia and the Slovak Republic reported the least frequent use. [END]
I should note that the statements below are typical of those used to identify memorisation strategies:
- I go over some problems in mathematics so often that I feel as if I could solve them in my sleep (sleep).
- When I study for mathematics, I try to learn the answers to problems off by heart (heart).
- In order to remember the method for solving a mathematics problem, I go through the examples again and again (examples).
- To learn mathematics, I try to remember every step in a procedure (procedure).
Seems reasonable, right? Perhaps what you were taught? Well it isn't! Agreeing with these statements relates to lower performance.
Note that NZ and Australia had the second highest memorisation responses (35%). The myth that the Asian countries follow a drill and skill approach is wrong. We are closer to that description! Their learners appear more self-sufficient and able to learn. Not so NZ learners. We seem to have bought into rehearsal strategies, despite the rhetoric from the MoE.
This study raises serious questions about what is really happening in classes at a social level. We need to start teaching learners to elaborate and control, otherwise we will continue to drop in the world rankings, and it’s getting pretty damn embarrassing!