Category: Professional practice
|Teaching and Learning Forum 2010 [ Refereed papers ]|
Edith Cowan University
This paper reports some of the findings of doctoral research into an approach to addressing concerns about low levels of numeracy amongst pre-service teachers. When someone is told that his/her performance is not up to a required standard, there can be a tendency to react negatively and to lose confidence. The research involved the development, delivery and evaluation of a mathematics module within a first year unit that was designed to improve skills in a range of literacies without decreasing levels of confidence amongst the students. The unit Becoming Multiliterate was offered as part of the BEd (Primary) and BEd (Early Childhood Studies) courses at Edith Cowan University and entailed students completing diagnostic tasks in mathematics, writing and science at the start of the semester to identify their weaknesses. Students were then provided with targeted support to enable them to reach identified benchmarks. Given that teacher registration bodies are likely to introduce literacy and numeracy standards for graduating teachers in the near future, the strategies used could be applied to similar courses elsewhere.
Unfortunately, experience internationally, across Australia and at ECU in particular indicates that it cannot be assumed that pre-service primary teachers entering university will be competent in mathematics. This is not a new phenomenon. In 1949, Glennon reported, "those preparing to teach arithmetic in the elementary grades understood only approximately 50% of the computational processes commonly taught in grades one through six" (cited in Rech, Hartzell & Stephens, 1993, p141). Hungerford (1994) quotes Leitzer (1991): "... the mathematical preparation of elementary school teachers is perhaps the weakest link in our nation's entire system of mathematics education" (p 15). The Australian Academy of Science identified mathematics as a "critical skill for Australia's future" and recommended that "all mathematics teachers in Australian schools have appropriate training in the disciplines of mathematics and statistics" with "national accreditation standards for teachers of mathematics at all levels of schooling.. and.. appropriate programs to ensure that future teachers meet these standards" (Rubinstein, 2006, p15). The Queensland Government recently supported a recommendation from the Masters Review that teachers be able to meet mathematics competence requirements in order to gain registration and has set timelines for the development and introduction of suitable tests (Queensland Department of Education and Training, 2009). Other states, including Western Australia, are likely to follow a similar path.
Despite the concerns, the benefits of administering entry diagnostic tasks could not be denied. Able students who could demonstrate the requisite levels of achievement would be recognised and allowed exemptions from remedial sessions, while those with only a few areas of concern would have targeted support provided. Those who needed more help would be identified and offered more intensive assistance. The agreed approach was based on the CRC model used by Toastmasters International in Australia (2008) when giving feedback to members developing public speaking skills. CRC stands for Commend, Recommend, Commend and places a strong emphasis on recognising what has already been achieved, providing advice and support for further development and recognising subsequent improvement.
While the focus of this paper is on the mathematics module, parallel processes were followed in writing and science and this had the added advantage of enabling students who were weak in one area but strong in another to use their partial success to feel more positive.
In the entry task, students were asked to indicate how confident they felt about having answered each question correctly. This enabled tutors to identify students who were particularly lacking in confidence and target them for extra support and provided base data for comparison with levels at the end of the unit. A formatted sample of a question from the task is shown in Figure 1. The first column indicates the Question Number (7) and the number of marks available (3). The second column indicates the relevant outcome (M2: Convert among units within the metric system eg cm to m, kg to g). The third column contains the question and includes space for the answer to be written underneath. The final column includes a Likert scale used by the student to rate how confident they felt that they had answered the question correctly.
|M2||A craft class teacher needs to buy supplies for the students. One week she has to buy ribbon - all the same colour and width - and wants to find out how much she needs to get. She has notes with her students' orders with the following measurements on them: 30 cm, 45 mm, 1.2 m and 1 m 25 cm. how much does she need to buy altogether?
||1 2 3 4|
The marking scheme was developed in detail. Staff taught the module a number of times each semester as students rotated through the unit, so there was a high level of consistency.
The results of the entry tasks were given to the students in individual interviews. Tutors provided them with a checklist of the skills required in the unit with those linked to correct answers already highlighted as complete. This was the Commend stage of the approach.
Over a period of three weeks students attended workshops in a computer laboratory where they were able to work on the outcomes they had not already completed. Tutors suggested a range of strategies appropriate for each student (the Recommend stage) including hands on materials based on those used to teach mathematics in primary schools. Worksheets were available for those who preferred pen and paper approaches and care was taken to link all resources to the specific outcomes so students could focus on what they needed to practise. A mix of whole class teaching, small group work and individual practice was used according to need.
A major component of the intervention stage was the use of the Mathletics website. This had a number of advantages over similar products. In particular, staff were able to select topics from a bank of resources and customise a program to suit the needs of the students both in terms of content and level. There was some concern that students would find the site too childish so staff specifically monitored their reactions. As it transpired, the students felt unthreatened by the activities and engaged with the cartoon characters and various sound effects in much the same way as children in a classroom. The atmosphere in the laboratories was relaxed and even fun - not words usually associated with mathematics.
At the end of the three week module tutors checked with each student that they knew what they had still to complete to meet the unit requirements. In the final part of the third session students sat an exit assessment which exactly paralleled the entry task so there were no surprises. Each paper was individually prepared for the student with the questions they still needed to answer highlighted on the front. While time consuming for staff, students appreciated being treated as individual learners rather than being part of a one size fits all approach. As a further incentive, students knew that if they got a lower score in the exit task for a question they had to repeat, they would retain their previous score for that question, ie they would not go backwards. Results were communicated anonymously via Blackboard and most students reached the 75% benchmark at this stage. Even if they did not pass, their scores improved and the checklist of outcomes still to be addressed was shorter. This is the third stage, Commend subsequent achievement. Students then worked individually using the website and other resources until resit opportunities were held at the end of semester one and, if necessary, at the start of semester two.
|Number of students enrolled in unit||337||344||371||344|
|Met mathematics requirements on entry||38||11||19||6||19||5||19||6|
|Met mathematics requirements on exit||250||74||228||66||246||66||262||76|
|Mean score on entry (out of 100)||51.1||45.7||47.0||36.9|
|Mean score on exit (out of 100)||78.4||76.9||77.4||71.2|
Data on levels of confidence on exit from the unit was collected at the start of the first mathematics education unit in semester two and compared to the entry confidence data elicited in the first assessment task. Figures are only available for 2006 and 2007 due to course structure changes and staff leave requirements. However, as can be seen in Table 2, the aim of addressing the need to improve competence without negatively impacting on confidence appears to have been successful.
|Mean confidence level on entry||71.5||65.3|
|Mean confidence level on exit||85.1||79.2|
Additional evidence related to student attitudes was gleaned from the data provided by the university Unit and Teaching Effectiveness Instrument. Selected results for the years 2006 and 2007, chosen on the basis of relevance to this paper, are shown in Table 3 below:
|The unit enhanced my knowledge and skills in the subject.||2006||87||303|
|The assessments assisted my learning.||2006||84||302|
|The lecturer catered for my individual needs in this unit.||2006||80||156|
|The tutor encouraged and supported my learning.||2006||93||206|
|The tutor provided useful feedback and guidance on my work.||2006||90||206|
|Overall I was satisfied with the teaching of this tutor*||2006||76||95|
|Faculty - overall satisfaction (tutor)*||2006||62||88|
|* Tutor overall satisfaction is used as it is based solely on the mathematics module.|
The low response rates for 2007 coincide with the introduction of online surveys and it was difficult to accommodate the modular nature of the unit in the new system. However, results are consistent across the two years indicating high levels of student satisfaction which compare well with results across the Faculty.
Students' written comments in the UTEI were also supportive of the approach that was taken in the unit. Over the two years 29% of responses commented positively on the use of the Mathletics site and 29% stated the unit had improved or refreshed skills, knowledge or understanding. The individualised or self paced nature of the unit, the identification and targeting of weaknesses, the easy to access resources and the helpful knowledgeable tutors were all mentioned in at least 10% of the comments. About 35% of written responses referred to the tutors always being available and willing to help, an acknowledgment of the key role they played in ensuring students maintained positive attitudes towards developing their mathematical skills.
Of course, it is not possible to satisfy everyone. Responses to the question What changes would you suggest for this unit? came from fewer students (83 over two years compared to 131 who wrote positive comments) and of these 45% wanted more time for the tests and/or more time to work on improvements. There were only a few comments in response to the question, Would you have liked this tutor to have done anything differently? but the following are typical.
Maybe more group work.A number of concerns must have been addressed following 2006, as more than a third of the responses to these questions in 2007 were "Nothing".
More checks on progress.
Do more examples on the blackboard.
Less online material and more practical application to help understand concepts.
The UTEI comments are perhaps best summed up in the following words written by a student in answer to the question, What aspect of this tutor's approach to teaching best helped your learning?
Her enthusiasm was awesome, she made me enjoy maths which I usually hate. I liked her availability, no question was too hard or too stupid. She explained why, how etc without making me feel inadequate, which is how I usually feel in mathematics.
Enochs, L. G., Smith, P. L., & Huinker, D. (2000). Establishing factorial validity of the Mathematics Teaching Efficacy Beliefs Instrument. School Science and Mathematics, 100(4), 194-202.
Flowers, J., Kline, K., & Rubenstein, R. N. (2003). Developing teachers' computational fluency: Examples in subtraction. Teaching Children Mathematics, 9(6), 330.
Hungerford, T. W. (1994). Future elementary teachers: The neglected constituency. The American Mathematical Monthly, 101(1), 15-21.
Kemp, M., & Hogan, J. (2006). Planning for an emphasis on numeracy in the curriculum. [viewed 9 Aug 2007 at http://www.thenetwork.sa.edu.au/pages/educators/articles_papers_index/, verifed 22 Jan 2009 at http://www.aamt.edu.au/content/download/1251/25266/file/kemp-hog.pdf
Latiolais, M. P., Collins, A., Baloch, Z., & Loewi, D. (2003). Assessing quantitative literacy needs across the university. Portland State University Faculty Focus, 14(1). [verified 22 Jan 2009] http://www.maa.org/SAUM/cases/latiolais-baloch-loewi1105-saum.pdf
Malinsky, M., Ross, A., Pannells, T., & McJunkin, M. (2006). Math anxiety in pre-service elementary school teachers. Education, 127(2), 274-279.
Queensland Department of Education and Training. (2009). Government response to the report of the Queensland Education Performance Review - 'Masters Review'. Queensland Government. (Retrieved 20/09/2009) http://education.qld.gov.au/mastersreview/pdfs/gov-response-masters-review.pdf
Rech, J., Hartzell, J., & Stephens, L. (1993). Comparisons of mathematical competencies and attitudes of elementary mathematics majors with established norms of a general college population. School Science and Mathematics, 93(3), 141-144.
Rubinstein, H. (2006). Mathematics and statistics: Critical skills for Australia's future. Key findings and recommendations of the National Strategic Review of Mathematical Sciences Research in Australia. Melbourne: Australian Academy of Science.
Sanders, S. E., & Morris, H. (2000). Exposing student teachers' content knowledge: Empowerment or debilitation? Educational Studies, 26(4), 397-408.
Steen, L. A. (2001). Mathematics and democracy: The case for quantitative literacy. National Council on Education and the Disciplines, Woodrow Wilson National Fellowship Foundation.
Toastmasters International in Australia (2008). The CRC. (Retrieved 14/08/2008) http://toastmastersvq.net/evaluationguide/
|Author: Brenda Hamlett, School of Education, Edith Cowan University. Email: email@example.com
Please cite as: Hamlett, B. (2010). Supporting pre-service primary teachers to improve their mathematics content knowledge. In Educating for sustainability. Proceedings of the 19th Annual Teaching Learning Forum, 28-29 January 2010. Perth: Edith Cowan University. http://otl.curtin.edu.au/tlf/tlf2010/refereed/hamlett.html
Copyright 2010 Brenda Hamlett. The author assigns to the TL Forum and not for profit educational institutions a non-exclusive licence to reproduce this article for personal use or for institutional teaching and learning purposes, in any format, provided that the article is used and cited in accordance with the usual academic conventions.