Poor mathematics performance in South Africa is well known. The COVID19 pandemic was expected to exacerbate the situation.
To investigate Grade 7 learners’ mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic.
Data were collected in term four of 2020 at 11 primary schools and five secondary schools. All schools drew learners from poor communities in Gauteng.
A multiplechoice test covering mathematical content from Grades 4–7 was designed and piloted. Learner performance was measured through number of correct responses. Qualitative error analyses were conducted on learners’ choices of distractors.
The difference in performance of the two grade groups was not statistically significant. There were similar response patterns in learners’ choices of distractors with strong evidence of cuebased reasoning and evidence of additive reasoning in items requiring multiplicative reasoning.
Grade 8 learners made very small gains, likely due to reduced learning time. Learner errors show many similarities with the international literature and show that Grade 7 learners are not yet ready for algebra.
The findings provide starting points for addressing the most common errors and highlight the need for: greater attention to whole and rational number concepts in Grade 8; strategies for teacher support in teaching primary maths content; and innovative teaching strategies to fasttrack learning of this content.
The COVID19 pandemic had a substantial impact on mathematics teaching and learning in South African schools in 2020 and 2021, particularly in poor communities where online learning was not possible. This loss of learning opportunities is likely to have knockon effects for several years to come because of the hierarchical nature of mathematics. In the last quarter of 2020, the Wits Maths Connect Secondary (WMCS) project, in partnership with the Gauteng Department of Education (GDE) and Olico Maths Education, developed and piloted a baseline assessment of Grade 7 learners’ mathematical knowledge to provide an indicator of what mathematics Grade 7 learners were bringing to high school at the start of the 2021 school year. Given the dual purpose of the test as both a
A group of Grade 8 learners were included in the pilot to compare with the Grade 7s. This stemmed from concerns that Grade 8s had very limited learning opportunities as a result of school closures from midMarch to late August 2020. By contrast, Grade 7s had returned to school in June 2020, although schools were then closed for another month in late July. Based on the reduced opportunity to learn for Grade 8s, the authors wanted to investigate possible differences in performance across the two groups, suspecting that Grade 7s might outperform the Grade 8s on some items.
Therefore, the research questions that frame this article are as follows:
The authors work from the assumption that a diagnostic–baseline test instrument, consisting only of multiplechoice items (MCQs), provides useful insights into what mathematics learners know and can do. They show how the test provides insights into learners’ mathematical proficiency as evidenced through their responses to carefully constructed items with distractors that address common errors. The authors are well aware that learners may guess responses when they do not know the answer but, as the study analysis will show, the trends which emerge from the data are largely consistent and also reflect many of the errors and misconceptions reported in the local and international literature.
The goal of this study is not to bemoan poor learner performance, although there are patches in the article when the reader may feel weighed down by the extent of low performance. Nevertheless, the authors seek to:
establish a picture of what learners can do mathematically in the context of the pandemic;
identify typical learner errors in whole number, rational number and multiplicative reasoning; and
provide recommendations for curriculum and teaching that are informed by the study findings.
Baseline and diagnostic testing are types of formative assessment in that their aim is to inform and support teaching and learning (Black & Wiliam
The study’s indepth analysis of learner performance deals with whole number, rational number (which includes fraction, decimal fraction, ratio, rate and percentage) and multiplicative reasoning. An overview of the relevant literature is provided which informed the item design in 2020 and now informs the discussion of learner test performance. The study focuses particularly on those aspects of primary school number work that are foundational for high school mathematics. These have been grouped into three themes: relational approach to working with numbers, multiplicative reasoning and rational number constructs.
Following Carpenter et al. (
This approach to number work, which moves beyond procedures and pays attention to the underlying functional relationships and structures, is crucial to learners’ future mathematical success (Cai & Knuth
This study adopts Steffe’s (
Fractions and rational number reasoning are necessary precursors to learners’ success in algebra (Confrey
Several common errors in fractions can be attributed to the overgeneralisation of wholenumber knowledge. These errors include adding two fractions by adding numerators and adding denominators, for example:
Similarly, several errors in working with decimals have their origins in overgeneralising from whole number knowledge (Durkin & RittleJohnson
Finally, a vital aspect in the development of numerical knowledge is an appreciation that all real numbers have magnitudes and can therefore be placed on the number line (Resnick, Newcombe & Shipley
Item selection and design was informed by the literature discussed above, as well as literature relating to the other topics not discussed in this article. Given the widespread low levels of performance in Senior Phase mathematics, the authors decided to include items spanning the curricula of Grades 4–7, with a small number of items on Grade 8 algebra. It was anticipated that this would indicate whether learners had mastered content of earlier grades and if not, what kinds of errors they made. It was also hoped that by including content from earlier grades, it might avoid the flooring effects that dominated South African learner performance in the Trends in Mathematics and Science Study (TIMSS) assessments (Bowie et al.
It was decided to use only MCQs because these could be marked quickly and thus reduce turnaround time for reporting results to schools when the test is implemented in the future. Each MCQ item was carefully chosen and designed to include distractors that reflect typical errors and/or misconceptions as identified in teaching practice and in the local and international literature.
A database of items was created, drawing from a range of existing sources, including released items from TIMSS, Olico’s existing item data base, items from the DBE diagnostic assessments, ANAs for Grade 6 and DBE Baseline assessments of 2020, as well as items gathered from baseline assessments of local schools. Items were separated into five topics: whole number properties and operations; rational numbers (fractions, decimals, percent, ratio and rate); patterns, functions and introductory algebra; measurement and geometry.
The topics were weighted differently based on their relative importance as foundational for Grade 8 mathematics. Number concepts and operations (whole numbers and fractions) constituted approximately twothirds of the items. The pilot instrument contained 66 items with weightings, as indicated in
Topic weightings for DiBa test pilot instrument.
Variable  Number of items  Total (%) 

Whole number operations  23  34.8 
Rational numbers (fractions, decimals, percent, ratio, rate)  20  30.3 
Patterns, functions and introductory algebra  10  15.2 
Measurement  8  12.1 
Geometry  5  7.6 
Two examples of test items are given below, dealing with decimal numbers and ratio.
In
Test item to identify largest decimal fraction.
For the ratio item, learners were required to calculate the number of pens in a collection; in a teacher’s stationery box, the ratio of pens to pencils is 5:4. If there are 36 pens and pencils altogether in the box, how many pens are there?
The options were:
A: 5 The stated ‘number of pens’ in the ratio
B: 18 Half of the total, that is 36 ÷ 2
C: 16 Number of pencils in the collection
D: 20 Number of pens in the collection (correct answer)
This question depends heavily on multiplicative reasoning. In order to identify the correct option, learners first need to recognise that 5 and 4 do not refer to actual numbers of pens and pencils, respectively. In order to select 20, not 16, learners must pay attention to the wording of the item and to the relationships in the notation (i.e. pens to pencils is 5:4) and recognise that the first number is related to pens.
One of the design features was to choose numbers in such a way that the distractors could be written as whole numbers and hence not in the same numerical form as the question. The intention was to check whether learners could recognise the correct answer even if its form did not match that of the question. For example, in the item on multiplication of fractions, two distractors were given in fraction form and two were given as whole numbers, one of which was the correct answer.
After completing a draft test instrument (hereafter test X), a parallel version (hereafter test Y) was designed with the same topic weightings. No anchor items were included because the goal was to pilot the items, not the instrument as a whole, and hence the authors wanted to pilot as many items as possible. The sequence of the items was partially adjusted so that the equivalent items on the last two pages of test X were moved into the middle of test Y to ensure that learners had time to attempt them (in case the test proved to be too long for the allocated time).
With special permission from the GDE because of COVID19related restrictions, the test was administered in late October and early November 2020 in four districts in the Gauteng province. The authors tested 473 Grade 7 learners in 11 schools, and 116 Grade 8 learners in 5 schools. The Grade 7 learners were closest to the target sample for intended future research, that is, Grade 8 learners entering high school. On the other hand, the Grade 8 sample provided an indication of learner performance at the end of the first year of high school, thus potentially providing evidence of change in mathematical performance over the year, albeit one that was substantially disrupted by the COVID19 pandemic.
Both versions of the test were piloted under typical test conditions. Learners were given approximately one hour to write the test. Feedback from invigilators and analysis of the scripts suggests that this was sufficient time to complete the test for both Grade 7s and 8s.
Learners wrote their responses on a preprepared answer grid, which was then scanned and processed by an online learner management system. Accuracy checks of the scanned images showed that approximately 10% of answer sheets were not scanned with 100% accuracy and therefore required manual capture of the learners’ responses.
An application for full ethical approval was made to the Human Research Ethics Committee (nonmedical) of the University of the Witwatersrand and ethical approval was received on 16 October 2020 (reference number HR20/10/32). Informed written consent was obtained from the parents of study participants. Informed written assent was obtained from learner participants. Schools were assured of anonymity and that their performance would not be compared with that of other participating schools.
In preparing the data for analysis, the authors resequenced the items from Test Y to correspond with those of Test X. All references to item numbers in this article refer to the item’s number in Test X. Data cleaning and processing revealed that the maximum percentage of blank responses was 5.4% per item with a mean of 2.8%. This indicated that learners would not have benefited from additional time. The maximum percentage of ‘bad’ responses, where learners selected more than one distractor, was 2.8% with a mean of 0.9%.
The performance of the items is not reported here, rather the focus is on learner performance, beginning with overall test performance, then performance per topic and then per item. This includes analysis of performance on each distractor. When comparing performance across grades, the
In the next section, the article reports first on overall performances. All comparisons across grades are made with caution, given the vastly different sample sizes. In the more detailed discussions of learner performance on specific items, attention is paid to grade differences where appropriate.
The overall learner performance was poorer than anticipated, with an average score of 35.8% and approximately 70% of learners achieving 40% or below (see
Distribution of learner test scores.
The average score for the Grade 7 group was 35.3%, with an average of 38.1% for the Grade 8 group.
Learner performance per grade per topic.
Number of learners  Number of items  Correct (%) 


Total ( 
Grade 7 ( 
Grade 8 ( 

Whole numbers and whole number operations  23  39.3  39.0  40.8 
Rational numbers  20  34.4  33.9  36.7 
Patterns, functions, algebra  10  37.7  36.2  44.1 
Measurement  8  26.3  26.3  26.4 
Geometry  5  36.7  36.4  38.3 
When comparing performance across grades, the differences in the mean weighted scores for each topic cluster are small, with the exception of
In this section, learner performance is reported on items involving whole number, rational number and multiplicative reasoning. Each section begins with overall performance together with a comparison of performance of the two grade groups. Thereafter, error analyses of clusters of items and/or selected individual items are provided.
Performance on whole number items for the entire group ranged from 77.8% down to 18.7%, indicating a wide variation in learners’ proficiency in different aspects of whole number properties and operations. There were only four items where more than 50% of Grade 7 learners answered correctly, and only six items where more than 50% of Grade 8 learners answered correctly. As noted above, the authors had expected better overall performance on whole number items because almost all of them dealt with content of Grades 4–6.
There is evidence that learners still lack understanding of the fundamentals of whole number operations such as order of operations and place value. For example, learners had to calculate: 8 + 20 ÷ 4. Only 22.2% of all learners selected the correct answer with the most common error being that of lefttoright reasoning where learners ignored the priority of division over addition, thus getting an answer of 7. Another item involved ‘horizontal addition’ to calculate the sum of 29 998 and 5. By far the most common error in both grades (approximately 20%) was to add 8 and 5 and append this sum to 29 998, giving 299 913. This error suggests many learners do not have a sense of number magnitude and are not paying attention to place value of the digits. A third item involved vertical subtraction with regrouping and borrowing with a partially missing minuend. This item is more cognitively demanding than merely calculating the difference of two 3digit numbers. The authors discuss the responses in detail because the errors reveal learners’ fragmented understanding of the procedures for column arithmetic.
Learners were required to work out the digits represented by ⊙ and □:
Only 34.8% of learners selected the correct answer, ⊙ = 8; □ = 5. Learners appear to be focused on ‘filling the blanks’ and thus chose methods of achieving this but showed little evidence of proficiency in column subtraction with 3digit numbers. Most learners appeared to focus on isolated parts of the problem. Approximately 21% appear to have used subtraction with missing subtrahends but were not consistent in assigning the minuend and the subtrahend in each column. For example, in the unitscolumn they seemingly worked
There were thee items involving whole number where the Grade 8s outperformed the Grade 7s by 10 percentage points (pp) or more. One of these items involved the square root of an even perfect square, for example
One of the items in which Grade 7s performed better than Grade 8s involved adding powers: 3^{2} + 3^{3}. This was somewhat surprising, because there is an emphasis on powers and exponents in the first term of Grade 8. Two distractors were given in power form and two as whole numbers. Only 28.2% of Grade 7 learners chose the correct answer (36), with 54.5% choosing one of the incorrect answers in power form. Almost 60% of Grade 8s chose distractors in exponential form where the exponential law for multiplying same bases (
A noteworthy finding related to this item was that although Grade 7s had not been taught exponential laws, 36.2% added bases and exponents, thus choosing the option 6^{5}. This appears to be an intuitive response for learners who have not yet been taught exponential rules. It also reflects a tendency to work additively.
Learners’ responses to the whole number items discussed above show repeated evidence of cuebased reasoning (Boaler
There were only two rational number items where learner performance was above 50%. By contrast, performance was below 30% on nine items. The authors discuss the subtopics within rational numbers separately, showing how whole number reasoning dominates learners’ responses in all subtopics together with a prevalance of cuebased reasoning based on visual features and/or counting. In several cases, the response profiles of both grades are provided to illustrate the similarities in the profiles on rational number items.
When adding unit fractions with the same denominator, such as
Learners were given the following options, when multiplying two fractions, such as:
The response profile for both grades was very similar. Approximately 50% of learners chose option A, where the denominators had been correctly multiplied and the numerator was a relatively large number but not the product of 4 and 21. While fewer learners chose option B (24.9% in Grade 7 and 19.8% in Grade 8), this was still far higher than the percentage choosing the correct answer (approximately 12%). That learners default to a procedural approach is apparent here by their choice of options A and B. It appears that very few learners used relational thinking, that is, noticing that 2 divides into 4, and 7 divides into 21 to give
Learners’ responses to an item involving conversion from percent to common fraction also reflected cuebased reasoning linked to visual features of the distractors. Learners had to identify the fraction equivalent to 12%.
Response profiles for the common fraction equivalent to 12%.
Variable  Which fraction is equivalent to 12%? 


A: 
B: 
C: 
D: 

Grade 7 (%)  15.0  17.8  42.1  20.9 
Grade 8 (%)  8.6  19.0  44.0  25.0 
Response profiles for identifying the largest decimal number.
Variable  Choose the largest number 


A: 0.536  B: 0.0005  C: 0.91  D: 0.908  
Grade 7 (%)  8.7  20.5  29.4  38.9 
Grade 8 (%)  13.8  19.8  30.2  33.6 
The three items on decimals dealt with: identifying the largest of four decimal numbers; identifying a decimal number on a number line; and adding two decimals with different numbers of decimal digits. As indicated above, the distractors reflect typical errors involving both whole number reasoning and decimal reasoning.
While approximately 30% of both groups chose the correct answer (C), more learners, particularly in Grade 7, chose distractor D, thus reflecting whole number reasoning; that is, 908 is the largest number, as discussed above. Approximately 20% of both groups chose the longest number, hence evidence of the longerislarger error.
Learners were required to identify the decimal number represented by T on the number line (see
Representing decimals on a number line.
Response profile for decimal number on number line.
Variable  Distractors (%) 


A: 0.9  B: 0.306  C: 0.36  D: 0.06  
Grade 7 (%)  31.7  13.1  26.2  24.1 
Grade 8 (%)  29.3  17.2  23.3  27.6 
Approximately 55% of learners chose an option which suggests they were counting steps on the number line (A and D), starting at 0.3 but not paying attention to the scale of the diagram and/or to place value. For example, 31.7% of Grade 7s chose 0.9, suggesting they focused on the significant digits 3 and 6 when combining 0.3 and 6.
Similar reasoning was also evident when adding decimal numbers: 0.5 + 0.03. As shown in
Response profiles for: Add 0.5 + 0.03.
Variable  Distractors (%) 


A: 0.53  B: 0.8  C: 5.3  D: 0.053  
Grade 7 (%)  51.4  22.8  7.2  16.5 
Grade 8 (%)  41.4  27.6  7.8  19.0 
In both decimal items above, there is evidence of partially correct decimal reasoning. For example, learners who chose 0.06 in relation to the number line show some evidence of understanding decimal numbers in relation to scale. However, they did not attend to the larger unit of 0.3 when determining the position of T. Similarly, learners who chose 0.053 show some evidence of recognising place value when working with decimals of different lengths. However, in choosing 0.053, they may be confusing the algorithms for adding and mutiplying decimals, where the distractor reflects the sum of the decimal places in the multiplier and multiplicand when mutiplying.
Multiplicative reasoning lies at the heart of work with rate and ratio, but learners’ performance on these items reflected cuebased reasoning and counting. For example, learners were asked for the ratio of squares to circles (see
Diagram for ratio item.
Fiftyeight per cent of the whole group chose D, presumably because they counted 5 circles and 10 squares and then chose a ratio with these numbers. This would suggest, once again, that they are working with visual cues, that they have not mastered basic ratio tasks and that they are not paying attention to the
In the item shown in
Distractors for item involving shading parts of whole.
For the ratio item involving pens and pencils (see above), the response profiles of each grade are given in
Response profile for ratio item pens:pencils.
Variable  Distractors (%) 


A: Number in ratio 5  B: Half of total 18  C: Number of pencils 16  D: Number of pens 20  
Grade 7 (%)  8.5  34.0  22.8  32.1 
Grade 8 (%)  0.9  22.4  33.6  42.2 
The item was correctly answered by 42.2% of Grade 8s but only 32.1% of Grades 7s. The most frequent response among Grade 7s was to halve the total number (i.e. 18), whereas only 22.4% of Grades 8s chose this option. Approximately 75% of Grade 8s selected an option which suggests some attempt to calculate ratios from the given information (C and D). By contrast, only 55% of Grade 7s chose one of these options. This may suggest a shift from inappropriate and unsophisticated responses to more appropriate strategies involving multiplicative reasoning from Grade 7 to Grade 8.
The selection of items and learners’ responses presented above reflects a dominance of cuebased responses, many of which are based on visual aspects of the numbers and/or diagrams. There is also evidence of whole number reasoning in dealing with decimal fractions. In most items, the Grade 8s outperformed the Grade 7s, although the response profiles are mostly similar.
Items requiring multiplicative reasoning appeared across all topics. The authors focus here on three items which show a predominance of additive reasoning in items requiring multiplicative reasoning.
Learners were given a number pattern with a common ratio of 4: 8; ___; 32; 64.
Nearly 60% of Grade 8s answered this item correctly, compared to only 46.1% of Grade 7s. By far the most common error, made by more than 30% of Grade 7s and more than 20% of Grade 8s, reflected additive reasoning where learners chose the distractor 12, most likely obtained from 4 + 4 = 8 and 8 + 4 = 12. This choice of distractor also suggests that learners were not considering all the given terms because the gap between 12 and 32 is clearly not the same as the gap between 4, 8 and 12.
There was even stronger evidence of inappopriate additive reasoning in an item dealing with percentages. Learners were asked: ‘A pizza costs R80. You pay 20% less. How much do you pay?’ Approximately 45% of all learners chose the distractor R60, signalling that they were working additively, subtracting R20 from the original pizza price. In contrast, approximately 20% of Grade 7s and less than 30% of Grade 8s chose the correct answer. Both groups of learners performed poorly on all items involving percentages.
One of the items involving functional relationships required learners to provide the rule associating input values with output values. The rules were deliberately expressed in terms of inputs and outputs (rather than letters) so that learners who were not familiar with algebraic notation would have a better chance of making sense of the rules.
Choose the rule that produces the pattern in the table (see
(The rules are given in
Input and output values for functional relationship item.
Response profile for functional relationship represented in a table.
Variable  A: Output = input + 2  B: Output = input + 4  C: Output = input × 3  D: Output = input × 4 – 1 

Grade 7 (%)  9.7  18.2  27.9  40.6 
Grade 8 (%)  8.6  16.4  17.2  56.0 
As shown in
However, inappropriate additive reasoning was evident in that more than 25% of learners in each grade chose options A and B. Although B focused on the common difference between outputs, the rule was stated as
In designing the DiBa test, the intention was to avoid a flooring effect by developing and selecting items dealing with mathematical content from Grades 4–7. As can be seen, flooring effects were not avoided on many items. However, learners’ choice of distractors and the related error analysis provide insights into their performance that were not available in previous largescale national assessments such as the ANAs.
The selection of whole number and rational number items presented here suggests that many learners approach items at face value, paying attention to what is immediately visible, without appropriate consideration for the relationships between symbols, and a lack of awareness of relationships in the context of the expression, diagram and so on. Although multiplicative reasoning underlies large areas of work in high school mathematics, learners’ responses suggest that many still had difficulty reasoning multiplicatively.
There is also evidence that cuebased strategies, such as looking for a particular number (recall item with 12%) and looking for a particular
The design feature of ‘unexpected forms’ of numbers may have contributed to poor performance on some items. However, it is the presence of this feature which potentially provides insight into learners’ strategies for choosing distractors. When learners choose incorrect options with the expected form rather than correct answers with an unexpected form, it suggests that they are paying attention to peripheral features of the distactors and their thinking is not informed by a relational understanding of the relationships between the numbers in the item. It may also indicate that learners are not actually doing calculations to obtain answers when presented with an MCQ format.
Returning to the research questions framing this article, the authors have shown that, based on overall learner performance, the difference between the grades was not statistically significant. Given that the majority of items dealt with primary school content, this suggests that in general, Grade 8 learners’ knowledge of primary school mathematics did not improve substantially in 2020. There may be several reasons for this, but the most obvious is that Grade 8s had very little opportunity to attend school in 2020, and when they were at school, teachers were hardpressed to cover as much Grade 8 content as possible with little time to address gaps in learners’ knowledge of primary school mathematics. Similarly, the overall performance of Grade 7s was also impacted by lost teaching and learning time in 2020, although to a lesser extent than Grade 8s.
However, there is substantial evidence that learners are leaving primary school with many gaps in their mathematical knowledge and that these were not necessarily related to the pandemic. For example, the items on decimal fractions involved content prior to Grade 7. That learners are not proficient in primary school mathematics at the end of primary school is not a new finding. However, the error analysis made possible through the MCQ format provides insights into the nature of learners’ errors and hence gives direction for future interventions, at both the primary and high school levels. The authors noted many similarities in the response profiles of both grades to test items discussed in this article. The same is true for the majority of items across all topics in the test. Many of the errors concur with local and international research, but new findings such as learners’ response to the item involving squares and cubes provide insight into learners’ reasoning prior to instruction on exponents.
The DiBa results show the substantial mismatch between curriculum expectations and the levels at which learners are performing. In testing Grade 7 and 8 learners on mathematics from Grade 4 upwards, it was hoped that many more learners would perform better on items from the lower grades. Unfortunately, this was not the case, and so many Grade 7 learners, possibly the majority of Grade 7s, enter high school without the necessary mathematical preparation to cope. The limited time allocated in Grade 8 to recap Grade 7 mathematics does not adquately address these gaps. This study makes three related recommendations for high school mathematics. Of course, many recommendations could be made for primary mathematics, but they are not in focus here.
Firstly, the Grade 8 curriculum should be revised to address key concepts of whole numbers and rational numbers (from primary school) in greater depth. This is not the same as the ‘revision’ of number work that appears in the current curriculum and which currently takes the form of rapid coverage of a long list of content but does not address conceptual foundations such as placevalue and the relative size of numbers (particularly fractions, decimals and very large whole numbers). Secondly, targeted support must be provided for Grade 8 teachers in teaching this content in ways that address the missing fundamentals. Prior work with high school teachers has shown that they are not well equipped with the knowledge and skills to address learners’ gaps in number concepts from primary school. This support should be structured around online resources that are freely avaiable and which teachers can access in their own time. The resources should focus on
While it is clear that dedicated time needs to be provided to consolidate whole number and rational number concepts, it is clear that teachers cannot reteach the content from scratch. Also, it also seems reasonable to expect that many learners can grasp the content faster than is expected in the grade in which it is usually taught (because the learners are older and have learned more mathematics). Thus the third recommendation is that mathematically sound strategies need to be developed to teach the primary school content to older learners in timeefficient ways that focus on the key aspects. In addition, these stategies should build relational understanding and give attention to generalisation and structure to support learners in the transition to algebra. This may involve omitting some of the details from the primary school curriculum. For example, there is little value in spending time to practise multiplying two 3digit numbers in high school. Similarly there is little point in excessive time on multiplying mixed numbers, as this has limited relevance to the kinds of algebraic fractions learners will encounter from Grade 9 onwards. Once again, developing such strategies is not trivial, and they will first need to be identified and/or developed, then piloted and refined by experts.
In this article, the authors have presented an analysis of results from the piloting of the DiBa Test in November 2020 with Grade 7 and 8 learners in selected schools in Gauteng. The overall average learner score was below 40%, and there was little difference in overall learner performance between Grade 7 and Grade 8 learners. The most persistent finding is that learners’ choices of distractors were cuebased, focusing on numbers (at face value) without sufficient attention to the context of the numbers and the relationships between numbers in an item. These findings are consistent with previous research conducted by the WMCS project and the local and international literature. The recommendations made in the study are built on the assumption that high school teachers must pay greater attention to learners’ mathematical knowledge gaps but that teachers cannot be expected to do this without substantial support and professional development. This is a matter of urgency, not just to recover from the impact of the COVID19 pandemic but to address another kind of pandemic that continues to wreak havoc with learners’ future prospects in school, beyond school and in the economy more broadly.
The authors are indebted to Jaqui Luksmidas for creating a spreadsheet tool to summarise, analyse and report the quantitative aspects of the data.
The authors declare that they have no financial or personal relationship(s) that may have inappropriately influenced them in writing this article.
C.P. was the principal investigator and L.B. was a coinvestigator of this project. They jointly led the development of the test instrument. C.P. performed most of the data analysis and wrote most of the article. L.B. reviewed the analysis, wrote parts of the article and provided comment on all drafts of the article.
The data that support the findings of this study are available from corresponding author, C.P., upon request.
The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of any affiliated agency of the authors.
The authors use lookalike items, meaning that the items in the article reflect the key features of the actual test items with minor differences such as different numbers and letters.