This study reports on an intervention that was aimed at improving the content knowledge of first-year intermediate-phase education students at a South African university. The study gives some insight into preservice teachers’ perceptions of an online programme for the development of mathematics common content knowledge for teachers of mathematics in the intermediate grades. The effectiveness of the intervention programme was analysed according to Shapiro’s evaluation criteria for intervention research. The findings show that there has been a positive shift in preservice teachers’ common content knowledge but that there is much room for further development. The student teachers found the programme to be of great benefit with regard to the development of their mathematics knowledge as well as their confidence as future teachers of mathematics. The findings highlighted their disturbingly limited knowledge of mathematics content knowledge and pointed to the responsibility of teacher education departments at universities to implement sufficient maths content courses that will address the status quo of poor mathematics teaching in South African primary schools. The authors conclude that the students need to spend much more time on ‘catching up’ before they become teachers.

Given the high value placed on scarce skills in South Africa, such as engineering, medicine, finance and accounting, most top-performing learners will go into professions other than teaching, which is assumed to be less lucrative. The challenge for teacher training institutions then is that the applicant pool for B.Ed. degrees tends to comprise young people with relative poor content knowledge of mathematics (Spaull & Kotze ^{1}^{2}

The paper reports on a pilot project of an online mathematics ‘co-curricular’ enrichment course and how this course advanced common content knowledge of the first cohort of intermediate-phase student teachers in 2014. The programme was added to the existing curriculum and therefore described as ‘co-curricular’. It also reports on the value of the course according to the students themselves, by drawing on their qualitative responses to open-ended questions in a survey. The initiative was funded partly through the Faculty of Education and partly through

As teacher educators who prepare preservice teachers for the foundation phase and as mathematics specialists for the intermediate phase, we believe that a strong basis of fundamental mathematics knowledge is vital. Our emphasis on the development of sound mathematical content knowledge is informed by the research findings on the strong correlation between teachers’ ability to teach and their MCK (Ball, Hill & Bass

Teaching in general is informed by various knowledge domains (Shulman,

In the last decade, the aim of mathematics education research has been to find out which national and institutional policies have most influenced the development of preservice professional knowledge. There has also been a keen interest in studying the influence of affective factors (e.g. self-efficacy beliefs, attitudes, maths anxiety) on the development of preservice teachers’ MCK and MPCK (Bandalos, Yates & Thorndike-Christ

A number of authors, in turn, did follow-up studies to explore factors associated with the development of preservice teachers’ MCK and MPCK. These studies looked at cognitive factors (MCK, MPCK and general pedagogical knowledge-GPK), individual predictors (e.g. gender effects, language effects, prior knowledge and motivation effects) and institutional predictors (sequencing and delivering of curriculum and practicum involvement). For the purposes of the paper, we briefly discuss two of these studies that highlighted the effects of preservice teachers’ prior mathematical knowledge on the development of their MCK.

Qian and Youngs (

Laschke (

assessing preservice teachers’ initial levels of conceptual and procedural knowledge as well as their levels of high school mathematics may help determine how much preparation via a mathematics methods course or other courses are needed to improve pre-service teacher’s conceptual mathematical knowledge. (p. 72)

A number of teacher education institutions have competency tests and student support courses in place to address preservice teachers’ lack of mathematics content they need to teach (Afamasaga-Fuatai’I, Falo & Meyer

A similar study was conducted by Mays (

This intervention comprised a pre- and posttest, using a Grade 7 level test for mathematical competence assessment. Because there was no control group and because the participants were not selected randomly, the study may be described as a ‘nonexperiment’. The effects of the intervention will be described by the four characteristics of Shapiro’s (

The intervention was administered after the baseline pretest to an intact intermediate-phase student–teacher group in the second half of their first year of study at the university (

Mathematics topic structure.

Topic | Number of Videos | Number of exercises completed by students |
---|---|---|

1. Addition and subtraction | 18 | 8 |

2. Multiplication and division | 42 | 16 |

3. Factors and multiples | 19 | 11 |

4. Negative numbers | 22 | 12 |

5. Fractions | 73 | 45 |

6. Decimals | 77 | 37 |

7. Exponents | 38 | 19 |

8. Arithmetic properties | 41 | 10 |

The average student mastered 137 exercises and watched 37 Khan Academy videos over the course of 10 weeks. In order to be considered to have ‘mastered’ a given exercise, students must complete seven questions correctly in a row. If they answered one question wrong, the exercise resets. In this way, Khan Academy encourages 100% mastery as opposed to the traditional 50% pass mark approach.

Whilst the target number of exercises was set at 150, students were encouraged to go beyond this target, with class prizes awarded to students who achieved the highest number of exercises mastered. The maximum number of exercises mastered by a single student was 231 (

Number of mastery exercises.

The average score on the baseline test was 37% [with a standard deviation (SD) of 11%]. The average score on the end-line test was 51% (with an SD of 13%). This constitutes an absolute shift of 14% upward, or roughly 1.16 SD from the mean.

Scores on pre- and post-test.

The student self-reporting survey consisted of a number of open-ended and closed questions. A, 5-point Likert scale was used for the open-ended questions. These questions included ones that asked students to respond to aspects such as the difficulty level of the exercises, usefulness of videos and improvement in mathematics competency levels. We present a synopsis of these data below.

Students were asked how they rated the difficulty level from (1) being easy, (2) easy-to-moderate, (3) moderate, (4) moderate-to-hard and (5) hard. Based on their responses, the overall difficulty rating for the course was 3.3 out of 5, indicating that the course was challenging but manageable (

Scores on pre- and post-test.

The following were some of the student responses on the open-ended questions about the difficulty level of the course:

The Khan Academy is very convenient and useful. It’s a very creative way to get students to pass Maths. It’s easy to understand.

Khan academy helped me to improve my maths skills and gave me easier methods of solving problems. Videos were very useful and mastery challenge too, although it was challenging.

Students were expected to spend 2 hours per week outside of class on the Khan Academy exercises and videos. These videos are instructional videos, where the mathematical concepts are explained and students have to complete an associated exercise. The average time spent watching videos was 5 hours per student over the 10-week period. Of the students, 84% indicated that they found the videos either ‘useful’ or ‘very useful’ (

Rating on usefulness of videos.

Some of the students’ responses were:

The course was useful because of the videos.

Videos were very useful and the mastery challenges as well.

Khan Academy was very useful to me and I have learned a lot from it, even though I don’t want to major in mathematics. I really enjoyed doing the activities given to me and the coaches were very good and well prepared on what they were doing.

Students indicated that they need more time working on the Khan Academy exercises. In all, 64% indicated that they preferred for the course to last the full semester of 14 weeks. Students indicated that they needed more time working through the exercises. The exercises were time bound and they thus felt that they could have completed more modules (

Duration of Khan Academy course.

The following are excerpts from students:

If we were given time for all this semester it was gonna be good and we would have completed all the exercises.

The Khan Academy was very useful to me because I learned too many skills that I will apply throughout the four years and further. One important thing I enjoyed learning is how to explain maths, which is going to be needed as a teacher.

It has created confidence in me because I can teach certain topics in various ways.

Khan Academy was very useful to me and it changed my negative attitudes towards mathematics.

Students were asked whether they think that their maths has improved as a result of the course. They rated their improvement from (1) no improvement, (2) slight improvement, (3) moderate improvement, (4) moderate-to-large improvement and (5) large improvement. Of the students, 78% indicated that the improvement of their maths ranged between moderate-to-large and large (

Effects of course on maths competence.

This program helped me a lot with maths concepts that I didn’t understand before.

The program helped me with a lot of things that I was failing in class but now I can do them with confidence. It changed the way I need to look at maths as being difficult. The good tutors helped.

Khan Academy was very useful to me I could not understand some of the things in class. Now I’m a little bit better in maths as I hate it.

I really learned a lot from Khan Academy even though I hated maths and I have always failed it but I managed to make sense of many things.

Of the 108 students in the course, only 38 were scheduled in major in mathematics at the outset of the course. At the end of the course, 14 students applied to change one of their majors to mathematics (

Percentage of students majoring in maths.

The evaluation process of this intervention study was guided by Shapiro’s (

We examine the intervention’s treatment effectiveness based on the actual effects of the preservice teachers’ participation on the development of their common content knowledge. The main finding of this pilot study shows that the intervention substantially improved the preservice teachers’ common content knowledge, with a very large 1.16 SD. This shift is significant at the

Proportion of Grade 3 students performing at the Grade 3 level by province and student quintile (Systemic Evaluation 2007).

Province | Proportion of Grade 3 students performing at the appropriate Grade 3 level^{a} |
Quintile | Proportion of Grade 3 students performing at the appropriate Grade 3 level^{a} |
---|---|---|---|

Eastern Cape | 17 | Quintile 1 | 10 |

Free State | 25 | Quintile 2 | 10 |

Gauteng | 26 | Quintile 3 | 12 |

KwaZulu-Natal | 13 | Quintile 4 | 29 |

Limpopo | 6 | Quintiles 1–4 | 11 |

Mpumalanga | 11 | Quintile 5 | 51 |

North West Province | 10 | - | - |

Northern Cape | 17 | - | - |

Western Cape | 32 | - | - |

South Africa | 16 | - | - |

Students are classified as performing at the grade-appropriate level if they obtain a mean score of 50% or higher on the full set of Grdae 3 level questions. Quintile 1 is the poorest 20% of students and Quintile 5 is the wealthiest 20% of students.

Preservice teachers were very involved in the mastery exercises and instructional videos with an average of 137 mastery exercises completed and 37 videos watched. There seems to be a strong correlation between prior knowledge (pretest) and number of mastery exercises completed in the participants. The participant with the highest pretest score of 73% managed to complete the maximum number of mastery exercises (231) and obtained an end-line score of 84%. This is likely because of the level of prior knowledge, which resulted in the participant completing the exercises at a faster pace and could thus complete more exercises. On the other end, the participant with a very low pretest score of 25% (not the lowest, lowest 17%) could only complete 67, the lowest number of mastery exercises in this study. This could be because of the number of times a particular exercise was reset because of a lack of conceptual understanding before moving on to a new exercise. The study found that the average preservice teacher spent one fifth of the time on watching the instructional videos and four fifths on mastering the exercises. This implies that preservice teachers with low prior mathematical knowledge need appropriate time to master new knowledge and skills. One of the biggest obstacles to student achievement is that these students started at a very low level of mathematical knowledge as indicated by the average score of 37% on the baseline test. However, the findings suggest that the intervention was effective based on the 1.16 shift in the SD from the mean. We are also clear that it is not possible to undo or remedy the lack in primary school mathematics in the 10 weeks of the intervention The low level of mathematics knowledge is likely because of the poor quality of their primary and secondary school mathematics education (refer to

Spaull and Kotze (

The trajectory lines, one for Quintile 5 and one for the average of Quintiles 1–4, show that in Grade 3 there already exist large differences in performance (approximately three grade levels) and that by the time children enter Grade 9, this gap in performance has grown to about four grade levels. The linear trend in performance between these two groups suggests that if the same number of students in Quintiles 1–4 in Grade 9 continued in schooling until Grade 12 (i.e. no drop out between these two periods), they would be functioning at approximately 4.5 grade levels lower than their Quintile 5 counterparts (1.4 standard deviations lower).

Social validity refers to the effectiveness of the Khan Academy programme as perceived by the preservice teachers. Students responded positively towards the intervention course. They indicated that the exercises were challenging but manageable. Responses like the following were given:

Khan Academy was very useful to me and I have learned a lot from it, even though I don’t want to major in mathematics. I really enjoyed doing the activities given to me and the coaches were very good and well prepared on what they were doing.

The course was found to be useful because of the instructional videos and mastery exercise and it is perceived to be a very creative way of learning mathematics. According to the students, the course improved their maths skills and they gained new methods to solve problems. Of the students, 78% reported that the improvement ranged between moderate-to-large and large. They also reported that the programme assisted them in understanding mathematics in their course work.

This program helped me a lot with maths concepts that I didn’t understand before.

The program helped me with a lot of things that I was failing in class but now I can do them with confidence. It changed the way I need to look at maths as being difficult. The good tutors helped.

The fact that 15 of the 108 students (14%) applied to change one of their majors to maths is a strong indicator of the increased enthusiasm and confidence students feel as a result of the intervention.

Treatment acceptability reports on whether the preservice teachers enjoyed the intervention procedure. Preservice teachers reported that they enjoyed the intervention, the instructional videos and the involvement of the course tutors:

Khan Academy was very useful to me and I have learned a lot from it, even though I don’t want to major in mathematics. I really enjoyed doing the activities given to me and the coaches were very good and well prepared on what they were doing.

However, they did feel that more time was needed and that they would have preferred for the course to continue for the full semester. According to a meta-analysis conducted by de Boer, Donker and van der Werf (

Treatment integrity refers to whether all preservice teachers who participated in the intervention received the same opportunities like access to the computer laboratories and effective coaches/tutors. Preservice teachers indicated that the coaches were skilled and very effective. The average attendance of the participants was 89%.There were some challenges as reported by the preservice teachers with regards to attendance; some found it challenging to attend these sessions because of financial constraints such as transport money because the sessions were not conducted on the same day as their lectures. All preservice teachers were given the same treatment and support.

The limitation of this study is that we did not analyse the knowledge gains within the different mathematical topics; factors and multiples, negative numbers, fractions, decimals, exponents, arithmetic properties and four basic mathematical operations. Because of the online nature of the course, it is also difficult to identify specific errors and misconceptions of specific content domains.

Implications for the Department of Childhood education would be to monitor and improve mathematics competency levels from year to year in order for preservice teachers to exit the programme with the requisite mastery competence. They would also be required to review and assess the appropriateness of the tutoring of at-risk students. Methodology lecturers should also review their methods courses to accommodate the lack in MCK.

It is evident to us that poor MCK of preservice teachers on entering teacher education programmes, especially the content knowledge they will have to teach to the learners, is not unique to the UJ Department of Childhood Education or South Africa. Preservice teachers in this study performed similarly in this intervention to their counterparts in other countries such as the USA, Australia, New Zealand, Germany, England and Canada. However, it is evident that as a department, we need to put unique interventions in place to remediate this lack in mathematical content knowledge of the pool of teacher education entrants.

Whilst not all preservice teachers would be specialising in mathematics, we argue that is important for all students teaching in the intermediate phase to have a firm understanding of the basics of mathematics. Thus, we do not consider this intervention as the whole solution to the low level of preservice teachers’ primary school mathematics in the UJ Department of Childhood Education. It merely highlights the fact that we need to pay attention to preservice teachers’ prior mathematical knowledge in order to make informed decisions about the type of mathematics content courses and methodology courses those of us in teacher education offer as learning opportunities.

On this basis, we conclude that this is an initiative worth investigating further. It is our contention that this intervention for childhood teacher education students can and does enhance the student experience of both the teaching and learning of mathematics.

The authors acknowledge the valuable contributions of the preliminary raw data from the online programme supplied by Mr Andrew Einhorn of Numeric.

The authors declare that they have no financial or personal relationships which may have inappropriately influenced them in writing this article.

K.F. (University of Johannesburg) and N.P. (University of Johannesburg) contributed equally to the writing of this article.

MCK ‘includes not only basic factual knowledge of mathematics but also conceptual knowledge of structuring and organising principles of mathematics as a discipline’ (Blömeke & Delaney 2012:225)

Mathematics pedagogical content knowledge is a blending of the MCK and a knowledge of how to make this content accessible to the students.