Engaging students in maths Patrick Barmby School of Education & CEM, Durham University

The aim of this part of the session Explore the notion of ‘engaging’ students in maths. Why? 10% drop in the take-up of A-level mathematics in the 1990s. Numbers in 2007/08 still about 6000 students down on the numbers taking the subject in STEM Mapping Review of 2004 identified over 470 STEM initiatives.

To start then… What does your school do to engage students in mathematics? (3 minute discussion with your neighbour then feedback)

What is engagement? The view from research: Newmann et al. (1992, p.12): “students’ psychological investment in and effort directed toward learning, understanding, or mastering the knowledge, skills, or crafts that academic work is intended to promote”.

What is engagement? Fredericks et al. (2004) highlighted three dimensions to engagement: behavioural, emotional/affective and cognitive. Behavioural ≡ Participation Emotional/affective ≡ Attitudes Cognitive ≡ Effort to comprehend

How can we develop engagement? Teachers; ‘Authentic’ instructional work; Meaningful problems with relevance; Student ownership of the work; Opportunities for collaboration; Challenging work which calls for understanding.

Tasks to try With your neighbour, choose one the problems presented on the sheet. (10 minute discussion with your neighbour then feedback)

Tasks to try - feedback Game of Nim –When picking up to 3 matches, the other person will lose if you leave them with 4n+1. –For a general maximum of picking up m matches, the other person will lose if you leave them with n(m+1)+1. A simple word problem… –Maria is 12, Laura is 18. A spot of bother… –258 spots (roughly) More importantly, did these engage you, or would they engage your students?

Engagement from secondary masterclasses From evaluation completed in July 2008; Masterclasses held in schools, universities, civic centres on Saturdays; Run by lecturers, guest speakers, PGCE students; Topic included: –Optimization of 2D and 3D shape dimensions; –Problem solving (carousel); –Being a paper magician; –The Power of Two; –Stick sculptures. 63% of the students agreed or strongly agreed that their attitude towards mathematics had improved due to the masterclasses. 70% of the students felt that their ability in mathematics had improved due to the masterclasses.

Quotes from students… “I like it, it is much better than what we do at school in some ways. Last week we had a class about rainbows, which was about the degree, the angle and so on. I didn’t know a rainbow could be mathematical! It combined maths and science. I like it much more now.” “Some of the things in school, you write the answers without even thinking, it’s easy. But here you really have to think about it.”

Quotes from students… “I don’t feel like a master either! If I was a master I would get all the problems straight off! But it does make me think. It doesn’t make me think I am amazing, it makes me think how I can solve this.”

The importance of problems/practical activities… “I just like puzzles, sometimes in maths you just get told stuff or you just have to work out things, whereas in those ones you’re actually making things and doing things that are imaginative.” “You learn yourself through experimenting rather than just being told something” “It is different methods and stuff and we put into practice Pythagoras’ theory and type of stuff. You cover it at school, but here you actually do it”

Engagement and understanding “A sample of middle school students reported higher cognitive engagement and greater use of learning and metacognitive strategies in classrooms where teachers presented challenging work and pressed for understanding” (Fredericks et al 2004: p. 75)

Engagement and understanding “We believe that the primary goals of mathematics learning are understanding and problem solving, and that these goals are inextricably related because learning mathematics with understanding is best supported by engaging in problem solving. The connection between solving problems and deepening understanding is symbiotic … in order to become a good problem solver, you need to have sound understanding. Thus, understanding enhances problem solving.” (Lester and Lambdin, 2004; p. 192)

Engagement and understanding  This is in line with the present focus on ‘understanding’:  Rose Review of the Primary Curriculum – the strand of Mathematical Understanding;  2008 OfSTED Report Mathematics: understanding the score;  Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools (Williams, 2008)

To conclude then…  Let us be clear about ‘engagement’;  The important role of problems and teaching for understanding.

Thank you!