Engaging students in maths Patrick Barmby School of Education

1
Engaging students in mathsPatrick BarmbySchool
of Education CEM, Durham University
2
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 1990.
• STEM Mapping Review of 2004 identified over 470
  STEM initiatives.

3
To start then

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

4
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.

5
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

6
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.

7
Tasks to try

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

8
Tasks to try - feedback

• Game of Nim
• When picking up to 3 matches, the other person
  will lose if you leave them with 4n1.
• For a general maximum of picking up m matches,
  the other person will lose if you leave them with
  n(m1)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?

9
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.

10
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 didnt 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, its easy. But
  here you really have to think about it.

11
Quotes from students

• I dont 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 doesnt make me
  think I am amazing, it makes me think how I can
  solve this.

12
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 youre 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

13
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)

14
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)

15
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)

16
To conclude then

• Let us be clear about engagement
• The important role of problems and teaching for
  understanding.

17
Thank you!