#### Home | Newsletter | Call for Papers | Register

#### How doLearners Construct Meaning when they Read Mathematics?: A Study of the Reading Difficulties Facing Foundation Phase Mathematics Learners in a Distance Learning Context

*Bohlmann Carol*.

Learning mathematics in English at a distance imposes unique challenges, especially for learners whose mother tongue is not English. Mathematics requires functional literacy and numeracy, academic skills, perseverance and self-discipline.

Mathematics has its own discourse, which imposes additional cognitive demands.

In distance learning students are required to construct meaning from text. Well-designed study guides show only end results and none of the (often messy) reasoning processes.

At Unisa in 2000 a joint project (Departments of Mathematics and Linguistics) investigated the extent to which poor reading skills undermined mathematical performance. The results showed that poor reading skills are a barrier to the successful study of text-based mathematics.

The second phase (2001) of the project involved the implementation of a reading intervention programme. There was a marked improvement in all reading skill components. Also, reading skill, as assessed in pretests, correlated most strongly with the final mathematics exam results.

The conceptualisation and implementation of the testing, as well as any intervention measures, are complex issues, especially in situations of cultural and linguistic diversity. They are relevant in determining what constitutes learning mathematics, and how the process can be improved.

Unlikely.

Mathematical understanding is developed through a reasoning process. In distance learning, students are required to construct meaning from text. Through the provision of well-designed study guides, students see only the end result: usually a well-presented piece of text, supported by attractive tables or graphics. They see none of the (often messy) chain of thought applied to achieve the solution to a problem. The study guides are written in as user-friendly a way as possible, and include written language help where it was felt that language issues may cloud mathematical issues. However, the “perfect” nature of the study material disguises the way in which mathematics is usually communicated in an oral teaching session. At this stage in South Africa, it would be discriminatory to provide only computer-mediated study material for this module, as it cannot be assumed that the majority of students have access to computers or videos.

Due to the wide range of topics that need to be covered, students are required to work through six study guides, a daunting task for those for whom reading to learn does not come easily.

Carol Bohlmann (Department of Mathematics, Applied Mathematics and Astronomy) and Lilli Pretorius (Department of Linguistics) both work at Unisa. In 2000 we began a joint project with the Departments of Mathematics and Linguistics to investigate the extent to which poor reading skills were undermining students’ mathematical performance. In 2000 we tested ideas regarding our perceptions reading problems with a volunteer group 25 students. After analysing their responses and refining the questions we sent a “Reading Skill Test” to all registered students in the access module (approximately 900). The test obtained some biographical information and investigated specific areas of reading difficulty, viz. vocabulary issues (use of low frequency words (academic and technical words)), anaphoric referencing, causal and contrastive relations in text, the ability to interpret visual information (simple tables and graphs). The returned tests showed a response rate of 45%. These results were analysed (the statistical package SPSS was used) and further compared with the exam mark obtained at the end of the year. Interesting statistics were obtained, showing a clear link between reading ability and academic performance. This does not imply that students who can read well will do well in mathematics; however it is clear that students who cannot read well will not be able to study mathematics effectively at a distance (using text-based material).

The project extended into 2001. This second phase involved the implementation of a reading intervention programme. We worked once a week for 22 weeks with another volunteer group of Mathematics Access Module students. Over the first three weeks biographical data was obtained from students through the use of questionnaires; pretests assessed their reading ability relative to the specific components that had been identified, and reading speed and comprehension tests were administered. The weekly activities involved extensive and intensive reading activities. The extensive activities (monitored each week) showed students how to take responsibility for their own vocabulary development, and encouraged them to read more widely and frequently. The intensive activities dealt with anaphoric resolution, text and sentence structure, causal and contrastive argumentation, and interpretation of tables and graph. The activities were introduced in a general context and then applied in a mathematical context. During the course of the programme personal interviews were conducted with students to assess their reading attitudes and practices. In spite of the relatively short duration and extent of the intervention programme, the posttests showed a marked improvement in all reading skill components. Reading speed and comprehension had improved as well.

To analyse the situation further, we compared the overall reading performance of the students against various school-leaving results (mother tongue, English, and mathematics) against their performance in mathematics assignments during the year, and against the final mathematics exam at the end of the year. We found that reading skill, as assessed in the pretests, correlated most strongly with their performance in the final mathematics exam. The implication of poorly developed reading skill as a barrier to academic success is significant, and further activities are now being undertaken to determine what intervention measures can be applied to the entire cohort of students registered for the module.

The research described above spans a period of two years. The impact of the measures introduced in 2002, and continued into 2003, is still being considered.

The complexity of the situation imposes unique demands regarding the conceptualisation and implementation of the testing as well as any intervention measures. All these issues fall under the umbrella of determining what constitutes learning mathematics, and how the process can be improved, but they appear to be relevant to learning in other areas as well. The results of the research thus appear to fit well into the overall theme of the conference. We would welcome the opportunity to share our ideas and interact with others who are operating in situations of cultural and linguistic diversity.

Mathematics has its own discourse, which imposes additional cognitive demands.

In distance learning students are required to construct meaning from text. Well-designed study guides show only end results and none of the (often messy) reasoning processes.

At Unisa in 2000 a joint project (Departments of Mathematics and Linguistics) investigated the extent to which poor reading skills undermined mathematical performance. The results showed that poor reading skills are a barrier to the successful study of text-based mathematics.

The second phase (2001) of the project involved the implementation of a reading intervention programme. There was a marked improvement in all reading skill components. Also, reading skill, as assessed in pretests, correlated most strongly with the final mathematics exam results.

The conceptualisation and implementation of the testing, as well as any intervention measures, are complex issues, especially in situations of cultural and linguistic diversity. They are relevant in determining what constitutes learning mathematics, and how the process can be improved.

Unlikely.

Mathematical understanding is developed through a reasoning process. In distance learning, students are required to construct meaning from text. Through the provision of well-designed study guides, students see only the end result: usually a well-presented piece of text, supported by attractive tables or graphics. They see none of the (often messy) chain of thought applied to achieve the solution to a problem. The study guides are written in as user-friendly a way as possible, and include written language help where it was felt that language issues may cloud mathematical issues. However, the “perfect” nature of the study material disguises the way in which mathematics is usually communicated in an oral teaching session. At this stage in South Africa, it would be discriminatory to provide only computer-mediated study material for this module, as it cannot be assumed that the majority of students have access to computers or videos.

Due to the wide range of topics that need to be covered, students are required to work through six study guides, a daunting task for those for whom reading to learn does not come easily.

Carol Bohlmann (Department of Mathematics, Applied Mathematics and Astronomy) and Lilli Pretorius (Department of Linguistics) both work at Unisa. In 2000 we began a joint project with the Departments of Mathematics and Linguistics to investigate the extent to which poor reading skills were undermining students’ mathematical performance. In 2000 we tested ideas regarding our perceptions reading problems with a volunteer group 25 students. After analysing their responses and refining the questions we sent a “Reading Skill Test” to all registered students in the access module (approximately 900). The test obtained some biographical information and investigated specific areas of reading difficulty, viz. vocabulary issues (use of low frequency words (academic and technical words)), anaphoric referencing, causal and contrastive relations in text, the ability to interpret visual information (simple tables and graphs). The returned tests showed a response rate of 45%. These results were analysed (the statistical package SPSS was used) and further compared with the exam mark obtained at the end of the year. Interesting statistics were obtained, showing a clear link between reading ability and academic performance. This does not imply that students who can read well will do well in mathematics; however it is clear that students who cannot read well will not be able to study mathematics effectively at a distance (using text-based material).

The project extended into 2001. This second phase involved the implementation of a reading intervention programme. We worked once a week for 22 weeks with another volunteer group of Mathematics Access Module students. Over the first three weeks biographical data was obtained from students through the use of questionnaires; pretests assessed their reading ability relative to the specific components that had been identified, and reading speed and comprehension tests were administered. The weekly activities involved extensive and intensive reading activities. The extensive activities (monitored each week) showed students how to take responsibility for their own vocabulary development, and encouraged them to read more widely and frequently. The intensive activities dealt with anaphoric resolution, text and sentence structure, causal and contrastive argumentation, and interpretation of tables and graph. The activities were introduced in a general context and then applied in a mathematical context. During the course of the programme personal interviews were conducted with students to assess their reading attitudes and practices. In spite of the relatively short duration and extent of the intervention programme, the posttests showed a marked improvement in all reading skill components. Reading speed and comprehension had improved as well.

To analyse the situation further, we compared the overall reading performance of the students against various school-leaving results (mother tongue, English, and mathematics) against their performance in mathematics assignments during the year, and against the final mathematics exam at the end of the year. We found that reading skill, as assessed in the pretests, correlated most strongly with their performance in the final mathematics exam. The implication of poorly developed reading skill as a barrier to academic success is significant, and further activities are now being undertaken to determine what intervention measures can be applied to the entire cohort of students registered for the module.

The research described above spans a period of two years. The impact of the measures introduced in 2002, and continued into 2003, is still being considered.

The complexity of the situation imposes unique demands regarding the conceptualisation and implementation of the testing as well as any intervention measures. All these issues fall under the umbrella of determining what constitutes learning mathematics, and how the process can be improved, but they appear to be relevant to learning in other areas as well. The results of the research thus appear to fit well into the overall theme of the conference. We would welcome the opportunity to share our ideas and interact with others who are operating in situations of cultural and linguistic diversity.

**Presenters**

**Bohlmann Carol**(South Africa)

*Lecturer in Mathematics*

Department of Mathematics, Applied Mathematics and Astronomy

University of South Africa

Department of Mathematics, Applied Mathematics and Astronomy

University of South Africa

**Keywords**

- University of South Africa
- Unique Challenges of Distance Learning
- Cultural and Linguistic Diversity
- Mathematics Access Module
- Mathematics: Cognitive Demands
- Mathematics Discourse
- Construction of Meaning from Text
- Joint Project: 2000 and 2001
- Departments of Mathematics and Linguistics
- Poor Reading Skills: Barrier to Mathematical Performance
- Reading Intervention Programme
- Extensive and Intensive Reading Activities
- Statistical Analysis
- Correlation Between Reading Skill and Mathematics Exam Results
- Complexity of Conceptualisation and Implementation of Testing and Intervention Measures

(30 min Conference Paper,
English)