Learning mathematics in this access course was ‘enjoyable’ - like eating ‘big slices of rich chocolate

gateau –I just gorged myself on it’

Barbara Miller-Reilly

University of Auckland

New Zealand

barbara@math.auckland.ac.nz

ALM 16 London July 2009

Research FocusAffective change in the students, relating this to their

achievement

• Overall marks, an accumulation of a range of assessment tasks, were used as a measure of achievement

To maximise strengths while overcoming weaknesses of qualitative and quantitative research approaches, appropriate qualitative and quantitative data were collected over several years (McLeod, 1994; Romburg, 1992)

• Hence affective change was investigated using Likert-style scales & open questions as well as interviews with selected students.

Literature

• Methods of instruction for adult learners of math: Fitzsimons and Godden (2000); Burton (1987).

• Affective issues: Damarin (1990); Buerk (1996); Goolsby et al (1987); McLeod D.B & McLeod S.H. (2002).

• Appropriate level and pace: Coben(1996); Munn, McDonald & Lowden (1992).

• Characteristics of learners at different stages of intellectual development: Boaler & Greeno (2000); Becker (1995); Buerk (1994); Magolda (1992) .

An access course: the Wellesley Program

A pre-degree full-time year-long certificate program- for 100 educationally disadvantaged students- all applicants were interviewed and took writing & maths tests- English & mathematics compulsory; two other subjects chosen- their mark in the maths test determined which of four groups (streams) students were taught maths in.

[Stream 1 – least maths background knowledge; Stream 4 – most maths knowledge.]

The maths tutors aimed to prepare adults for tertiary study with a carefully paced re-introduction to high school mathematics;

to build students’ confidence; to promote good study habits.

Difficulties

• Students have wide range of background mathematics

• Students often have difficult personal circumstances & few study skills

Many belong to the “under-educated” category - one of the four clientelle groups Smith(1990 p. 50) describes in adult education. He suggests that students in this category are “especially subject to anxiety and doubts about their learning ability and that “establishing a climate for minimizing anxiety” is the “most crucial condition for learning success in this population”.

Mathematics background knowledge &

achievement differences

The major effect on achievement was mathematics background knowledge, as measured by the entry

mathematics test.

Marks in this test determined which of the four groups (streams) students were taught in.

[Stream 1 – least math background knowledge; Stream 4 – most math knowledge.]

Hence, the affective data was analysed by streams, in particular, comparing stream 1 students with stream 4

students.

Differences and changes in beliefs; Reactions to course

• Most of the higher achieving group entered the course with more confident mathematical beliefs and reported feeling more mathematically confident by the end of the course than the lower achieving group. These differences were also reflected in the quantitative measures of attitudinal scales and of both their beliefs in themselves as learners of maths and beliefs about the learning of maths (Gourgey, 1982; Aiken, 1974; Schoenfeld, 1989) .

• Most of the lower achieving group not only entered the course indicating less confidence in, and enjoyment of, maths but also reported less confidence by the end of the course.

• Successful students were pleased with the amount of mathematics they had learned, much of which they had not understood in high school and, generally, found the pace suited them, even though for some it was reasonably challenging.

• Many lower-achieving students found the pace too fast.

High school etc

Mary Father got tutor for her in maths but still couldn‟t

understand. Her mother “wasn‟t very good at

maths either”. Left high school at age 15.

Hone Lost interest in school work - left high school at

age 16.

Parents “wanted me to get good education but

didn‟t push ya”

Diane “I was so quiet in school they didn‟t realise that I

couldn‟t read until high school!” “Always told I

was dumb.” “Always been quite good at maths”.

Completed 5 years of high school.

After high school …

Mary Baby (boy) at age 16. A few years later,

adult day student at high school –

passed 4th year hs subjects.

Hone Trade Training School: Butcher.

11 years overseas:

scaffolding, rigging, butchering.

Diane Army for 11 years: Supplier, Intelligence.

Married with 2 children aged 6 and 2.

Choosing the access course (the Wellesley Programme)

Mary Wanted to start a science degree.

Her son now 9 years old.

Hone Wanted to get some tertiary education. “Didn‟t

know whether I could handle it”. Interested in

“doing something in the health field”.

Diane Sick of the “boys club”! Always wanted to go to

university (cf sister). Had thought about doing

physiotherapy. Thought WP would give her an

introduction.

Stream placement, Belief in themselves as learners of maths, Final results

Mary Stream 3 asked to move to Stream 1

11 / 40 ------ 7 / 40 (among lowest)

30%

Hone Stream 2

20 / 40 ------ 18 / 40 He reported a gain in

confidence to an “acceptable” level.

60%

Diane Stream 3 wanted to move to Stream 4

31 / 40 ------ 38 / 40 (among highest)

89%

Mary’s method of learning math

• “I just wrote everything down, everything (the tutor) said, any method to do things. I wrote and I wrote. … When it came to studying it, I’d sit down and look at it – I’d refer to examples in the book and then I would just get confused. I couldn’t decide what which process to use for which equation. Then I'd get annoyed because I'd think that I had it, then I'd do an example and then something would go wrong. I'd sit there on one problem for ages, probably a few hours and quite often I'd just get confused. I wasn't achieving anything, just stressing myself out. Then I'd avoid it if I could.”

Mary seems to be a “passive receiver of knowledge” – a “received knower of math” (Becker, 1995; Boaler & Greeno, 2000)

Hone’s method of learning math

Hone: “the Wellesley Program is pretty challenging – I’d never done real education before” … “Well I ended up making friends on the course and a few of us had study groups. I used to organise them and have them around home – my sort of social thing, you know, invite people and then have a barbeque at the same time … it’s not so heavy – full on maths, have a break, go back and go back to it again, then throw it around each other by discussing it, compare methods – we would get a good bond that would make it more understandable.”

Hone seems to be a “subjective knower of math” (Becker, 1995; Boaler & Greeno, 2000; Buerk, 1994).

Diane’s method of learning math

Diane talked about how studying maths in WP was easy: “When I got an assignment in maths I’d go home & do it straight away because I knew I could do it, then it would be out of the way. In some other subjects, like English, I’d drag my feet.”

She said that the most important thing she learned was “starting to introduce problems”. Her teacher “quite often puts into real situation and you have to figure it out through maths”.

Diane seems to be an “independent knower of maths” (Magolda, 1992) or at a “systematic reasoning” stage of learning maths (Becker, 1995; Boaler & Greeno, 2000; Buerk, 1994) .

More information was gathered using metaphors (Gibson, 1994; Buerk, 1996).

Mary: “If maths were a … what kind of … would

it be?”

… food“Something disgusting – I hate meat – like a disgusting beef stew!”

… a way to

travel“It’s like a fast train – it’s going so fast and I‘m trying to understand what it’s doing –too fast!

“Not long into the first term I realised I was just taking off more than I could chew. … I learnt a lot through doing this, what not to do more than what to do”.

Diane: “What if your experience learning maths in WP were …?”

… food “Chocolate gateau! Rich every morning! I just gorged myself on it! I really enjoyed Wellesley maths!”

… a way to

travel

“It would be a nice train ride, steady, and you got there in the end, on time!”

Hone: “What if your experience learning maths in WP were …?”

… food

“It is an assortment of lollies …

depending on what lolly you eat, some

were sour, some were really sweet,

some were bitter … different kinds of

taste what lolly you pick”

… music

It was a bit of opera or classical music …

if you listen hard enough it‟s really nice,

as long as you don‟t prejudge it before

you listen to it”. My favourite music is

“reggae and soul but there‟s some things

in opera that have a different appeal in

a different way”

After Wellesley Programme …

Mary Planned to study part time for a

Certificate in Applied Science.

Hone Qualified as a Community Occupational

Therapist. He is now working in this field.

Diane MSc First Class Honours in biomedicine.

Now enrolled in a PhD in Obstetrics and

Gynaecology.

Further discussion

• Methods of instruction for adult learners of maths (Fitzsimons and Godden, 2000) “which focus on technique and

lack any overview, connectedness or historicity, together with an absence of community and manifestations of competitiveness rather than cooperation are discouraging to adult learners”

• Affective issues: Damarin (1990); Buerk (1996); Goolsby et al (1987); McLeod D.B & McLeod S.H. (2002). Minimizing anxiety important for adults returning to study – compare Mary’s experience with others.

• Appropriate level and pace: Coben(1996); Munn, McDonald & Lowden (1992). We can compare Mary’s experience with Hone’s and Diane’s.

References

Aiken, L. R. (1974). Two Scales of Attitude Toward Mathematics. Journal for Research in Mathematics Education, 5, 67-71.

Becker, J. R. (1995). Women's Ways of Knowing in Mathematics. In P. Rogers & G. Kaiser (Eds.), Equity in Mathematics Education: Influences of Feminism and Culture (pp. 163-174). London: The FalmerPress.

Boaler, J., & Greeno, J. G. (2000). Identity, Agency, and Knowing in Mathematics. In J. Boaler (Ed.), Multiple Perspectives in Mathematics Teaching and Learning (pp. 171-200). London: Ablex Publishing.

Buerk, D. (1996). Our Open Ears Can Open Minds: Listening To Women's Metaphors For Mathematics. Focus on Learning Problems in Mathematics, 18(1, 2 & 3), 26-32.

Buerk, D. (Ed.). (1994). Empowering Students by Promoting Active Learning in Mathematics. Reston, VA: The National Council of Teachers of Mathematics (NCTM), Inc.

Burton, L. (1987). From Failure to Success: Changing the Experience of Adult Learners of Mathematics. Educational Studies in Mathematics, 18, 305-316.

References

Coben, D. (1996, 9-11 October 1996). Putting Adults into the Equation: an Agenda for Adult Learning in Mathematics for the New Millennium. Mathematics for the new Millennium - What needs to be changed and why? from http://www.leeds.ac.uk/educol/documents/000000044.htm

Damarin, S. K. (1990). Teaching Mathematics: A Feminist Perspective. In C. R. H. Thomas J. Cooney (Ed.), Teaching and Learning Mathematics in the 1990s (pp. 144-151). Reston, Virginia 22091: National Council of Teachers of Mathematics.

FitzSimons, G. E., & Godden, G. L. (2000). Review of Research on Adults Learning Mathematics. In D. Coben, J. O'Donoghue & G. E. FitzSimons(Eds.), Perspectives on Adults Learning Mathematics: Research and Practice (pp. 13-45). Dordrecht: Kluwer Academic Publishers.

Gibson, H. (1994). "Math Is Like a Used Car": Metaphors Reveal Attitudes toward Mathematics. In D. Buerk (Ed.), Empowering Students by Promoting Active Learning in Mathematics (pp. 7-12). Reston, Virginia: The National Council of Teachers of Mathematics, Inc.

ReferencesGoolsby, C. B., Dwinell, P. L., Higbee, J. L., & Bretscher, A. S. (1987).

Factors Affecting Mathematics Achievement in High Risk College Students. Paper presented at the Annual meeting of the American Educational Research Association.

Gourgey, A. F. (1982). Development of a Scale for the Measurement of Self-Concept in Mathematics.Unpublished manuscript.

McLeod, D. B. (1994). Research on Affect and Mathematics Learning in the JRME: 1970 to the Present. Journal for Research in Mathematics Education, 25(6), 637-647.

McLeod, D. B., & McLeod, S. H. (2002). Synthesis - Beliefs and Mathematics Education: Implications for Learning, Teaching, and Research. In G. Leder, E. Pehkonen & G. Torner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp. 115-123). London: Kluwer Academic Publishers.

Miller-Reilly, B. (2006). Affective change in adult students in second chance mathematics courses: three different teaching approaches.Unpublished doctoral dissertation, University of Auckland, Auckland, New Zealand.

References

Miller-Reilly, B. (2008). Is „Connected Teaching‟ in Mathematics a Gender-Equitable Pedagogy for Adults? Adults Learning Mathematics - an International Journal, 3(1), 41-60.

Munn, P., MacDonald, C., & Lowden, K. (1992). Helping Adult Students Cope. Mature Students on Science, Mathematics and Engineering Courses (Reports - Research/Technical No. SCRE -RR -39). Edinburgh: Scottish Council for Research in Education.

Romberg, T. A. (1992). Perspectives on Scholarship and Research Methods. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 49-64). New York: Macmillan Publishing Company.

Schoenfeld, A. H. (1989). Explorations of Students' Mathematical Beliefs and Behavior. Journal for Research in Mathematics Education, 20(4), 338-355.

Smith, R. (1990). Learning How to Learn: Applied Theory for Adults. Milton Keynes: Open University Press.