Pierre Varly, Anthony Saarpong
This blog post address the issue of the poor performance of Ghana in Mathematic achievement in primary education. Ghana scores among the last countries in the TIMSS international assessment. The national education achievement (NEA) survey show important learning gaps in Mathematics for a decade. What are the national standards? Are these standards the same as in other countries? Are these national standards achieved by pupils? How well are teachers trained to teach maths? How do teachers teach maths? What are the future challenges and opportunities?
National standards
According to the national syllabus, in order to achieve the general aims of the Mathematics curriculum, teachers must provide opportunities for children to realize the specific minimum objectives which are the National Minimum Standards (NMS) for Primary 6 numeracy. NMS for Primary 6, which are the main terminal objectives for education, listed below are intended to give the teacher an idea of some of the things ALL the pupils should be able to do by the end of primary school. Some targets may be more complicated than they seem and so the syllabus has been designed for the teacher to revisit some of these objectives more than once in the year and possibly again at Junior High School (JHS) level.
At the end of grade 6, pupils are expected to:
- Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect.
- Order a mixed set of numbers with up to three decimal places.
- Reduce a fraction to its simplest form by dividing through by common factors.
- Use a fraction as an operator to find fractions of numbers or quantities (e.g. of 48, of 30, of 200 centimetres).
- Understand percentage as a number of parts in every 100, and find simple percentages of small whole-number quantities.
- Solve simple problems involving ratio and proportion.
- Carry out column addition and subtraction of numbers involving decimals, up to 3 decimal places.
- Derive quickly division facts corresponding to multiplication tables up to 10 × 10.
- Carry out short multiplication and division of numbers involving decimals.
- Carry out long multiplication of a three-digit by a two-digit integer.
- Use a protractor to measure acute and obtuse angles to the nearest degree.
- Calculate the perimeter and area of simple compound shapes that can be split into rectangles.
- Read and plot co-ordinates in all four quadrants.
- Identify and use the appropriate operations (including combinations of operations) to solve word problems involving numbers and quantities, and explain methods and reasoning.
- Solve a problem by extracting and interpreting information presented in tables, graphs and charts.
International issues in Mathematic curricula in upper primary grades (5 and 6)
The national syllabus is typically found in other African countries though it is organized by objective while many African curricula are now based on competency. At international level, analysis of national curricula showed that data representation and analysis, and proportionality are relatively new challenging in curricula worldwide and. More specifically collecting data; arraying them in simple tables and graphs; understanding simple measures of central tendency and dispersion; and sampling have only recently entered pre-service teacher training programs.
Proportionality and the attendant topics in the area of fractions represent some of the most abstract and challenging subjects in primary school Mathematics. They are considered vital to developing strong mathematical reasoning skills and represent the most cognitively demanding subjects in the primary school curriculum – often equally challenging for students and as it is for teachers. A number of authors observe that common and decimal fractions are the first serious exercises in the type of abstract mathematical reasoning.
Many common performance expectations are found in Mathematics across countries and document types. These shared skill standards mainly revolved around routine and basic skills in mathematical problem solving and reasoning but did not include more cognitively demanding Mathematics skills. Alignment between textbooks and intended curricula is low (maximum is 42%).
Are the national standards achieved ?: Learning results from NEA and EGRA tests
NEA
The NEA findings indicated that primary school pupils were challenged by both English and Mathematics, with no more than 37% of pupils achieving proficiency levels in any grade or subject.
Performance was noticeably lower for Mathematics than for English, with only 22% Ghana 2016 of P4 and 25% of P6 pupils achieving proficiency in Mathematics compared to 37% of P4 pupils and 36% of P6 pupils achieving proficiency in English. It is also important to highlight that for both grades and for English and Mathematics, at least 29% of the pupils failed to correctly answer 35% of the questions correctly, the cut-point for minimum competency. That is, 29% of the P4 English pupils and P6 Mathematics pupils, 30% of P6 English pupils, and 45% of P4 Mathematics pupils performed below the minimum competency level.
% pupils per category in maths (NEA)
Source : NEA report (2016)
The Numbers domain assessed how well pupils understood basic numerical expressions, such as place value, numerical symbols, and the use of a number line. The Measurement domain involved understanding basic measurement and applying measurement skills. The Shape and Space domain (Figure 10) involved understanding the basic properties of plane and solid shapes and using the skills to evaluate the relative size of shapes and spaces. The Operations domain involved having pupils compute basic mathematical operations involving addition, subtraction, multiplication, and division. The Data and Chance domain required applying Mathematics operations to data to perform ‘real life’ Mathematics problems and finding out how certain real life events occur.
Pupils demonstrated having the most difficulty with tasks in the Measurement domain and the Shape and Space domain, with Measurement tasks being particularly challenging (34% for P4 and 29% for P6) compared to Shape and Space (38% for P4 and 39% for P6), NEA (2016).
The results to the fraction sub domain was noticeably low.
% response correct by domain, by grade (NEA)
Source : NEA report (2016)
Boys and girls performed similarly in P4 mathematics. Although girls and boys also struggled with P6 mathematics, males outperformed females by two percentage points, a difference that, while not substantive, is statistically significant. Only 14% of P4 pupils and 18% of P6 pupils from rural areas achieved proficiency in Mathematics. With the exception of P6 mathematics, the majority of pupils in private schools in 2016 reached the proficiency level in both grades and subjects. In P4 Mathematics, 52% of pupils in private schools achieved proficiency in 2016, as opposed to 14% in public schools. In P6 mathematics, 47% of pupils in private schools achieved proficiency as opposed to 20% in public schools.
There was considerable variability in performance across regions, with distinctly lower performance for pupils attending schools in the three regions of northern Ghana (Northern, Upper East, Upper West) compared to pupils attending schools in other regions. As in previous NEA administrations, in general, pupils attending schools in Greater Accra were shown to outperform those in the other regions of the country. The relative proportion of pupils who achieved proficiency was highest in Greater Accra, for both grades and both subjects.
EGRA
The overall results for the EGMA survey are summarised in below. The EGMA showed that by the end of primary 2, pupils were doing reasonably well on the most procedural items—number identification, addition level 1 and subtraction level 1—with pupils scoring on average nearly 50% or better on these subtasks. That said, the pupils did better on addition level 1 than on subtraction level 1, with nearly 20% of the pupils unable to answer a single subtraction level 1 item correctly—the easiest of these items being: 4 – 1 = iiii.
When it came to the more conceptual items, the pupils still scored reasonably well on the quantity discrimination subtask. However, on the missing number, addition level 2 and subtraction level 2 subtasks, there was a sharp drop-off in performance, with nearly 70% of the pupils unable to answer a single subtraction level 2 item correctly—the easiest of these being: 19 – 6 = . This stark difference in performance between the procedural and conceptual subtasks suggests a lot about how children in Ghana are likely to experience school Mathematics. That is, it is likely that they experience Mathematics as a subject in which you have to know the answer rather than having a strategy for developing it: Mathematics as the memorisation of facts, rules and procedures.
Source : EGRA report (2013)
These results interrogate the level of preparedness for teachers to tech maths.
Teachers training
There are different categories of training in Mathematics. First, the Universities and the colleges of Education. The universities run a 4-year B.Ed degree in Basic Education. In this programme the students are given pedagogical training on how to teach Mathematics in basic schools together with other subjects taught at the basic level. Additionally, they are giving the option to specialize in at least one of the basic level subjects which can be Mathematics. There is a minimum of a semester teaching practice included in the programme.
The colleges of Education, traditionally mandated to train teachers for the basic schools, run a 3-year Diploma in Basic Education that consist of training in Mathematics that enables trainees to teach Mathematics at least in the primary school level. In the 3-year diploma, the first year is used to mostly cover Mathematics content similar to the Mathematics done in SHS. In second year, a 2-hour a week Mathematics methods or pedagogue and a 2-hour content is done for the two semesters. Thus primary methods for first semester and Junior high school methods for the second semester. There is also a one year teaching practice in a basic school included in the programme. On completion of the 3-year Diploma, teachers can upgrade to B Ed in Basic Education through sandwiched course and top ups that last for two years. Here, they are giving the option to specialize in a basic education subject which can be mathematics. However, only few opt for Mathematics.
The type of instruction learnt by future teachers are the activity, demonstration, group and hybrid/blended methods. Teachers also learn how to prepare teaching and learning materials for mathematics and improvisation. Despite this training, do teachers have enough content knoweledge to be able to teach properly ?
Teachers content knowledge
According to the STEP data survey that target urban adult population 15-64, in Ghana, only 20.3% of the primary teachers reach the minimum literacy level to teach and 36.2% in secondary (where 88.5% of teachers have tertiary education). While noting that the tests were administered in national languages, a fair proportion of teachers operate at literacy levels way below the minimum requirement.
The table below show teachers content knowledge in several African countries.
Teachers SDI scores by domain (% correct response)
Mozambique | Kenya | Nigeria* | Tanzania | Togo | Uganda | Average SDI | |
Mathematic (average core) | 33 | 77 | 42 | 65 | 33 | 58 | 55 |
Adding double digit numbers | 87 | 98 | 89 | 97 | 79 | 96 | 92 |
Subtracting double digits | 65 | 86 | 70 | 86 | 65 | 79 | 77 |
Comparing fractions | 17 | 40 | 16 | 50 | 13 | 21 | 28 |
Subtraction of decimal numbers | 39 | 83 | 45 | 67 | 18 | 57 | 54 |
Source : Mozambique SDI technical report.
Note: * Surveyed states in Nigeria are: Anambra, Bauchi, Ekiti, and Niger. |
The World Bank in its Service Delivery Indicators (SDI) survey do test teachers in language and Mathematics. Unfortunately, Ghana is not part of the recent data collection. However, the table above is quite descriptive of teachers’ content knowledge (grade 4 teachers).
Adding or subtracting two digit numbers strands have high score, but on average 8% of the teachers fail to add two digits and 23% fail to subtract two digits ( grade 2 or grade 3 pupil level items). Teachers are challenged with the fraction domain (only 28% correct response on average). The average scores are just above 50% of correct responses. Kenya teachers outperforms the other countries in the SDI survey and so are pupils in the SACMEQ and EGRA data collections. The situation is particulary challenging in Togo and Mozambique where 35% of the teachers fail to subtract two digits. How can these teachers properly teach ?
All this lead us to think, that the problems experienced by the pupils in Mathematics are driven by a poor content knowledge from teachers. Recent analysis (forthcoming) show that teachers pedagogical practices have a higher impact on children test scores than the teachers content knowledge.
Teaching methods in classroom
A study in the Winneba district found that, though there was rhetoric in the introduction of the curriculum materials on the use of discovery teaching methods, few learning/teaching activities that would encourage the use of such discovery methods were included in the materials. It was observed that both the official curriculum and the teachers who implement it emphasise expository teaching methods.
As a consequence of the infrequent use of teaching/learning materials and practical activities, pupils have little chance of asking questions. Just about 17 per cent of the teachers were found to have provided meaningful answers to pupils’ questions mainly because many of the teachers hardly engaged pupils in activities that will urge them to ask questions. Though about 70 per cent of the teachers were found to be teaching challenging Mathematics, as many as 98 per cent of them were found using solely examples and exercises set in the official textbooks. Teachers make pupils to use only the standard textbook methods irrespective of their abilities.
According to this study, Mathematics lessons in most classrooms visited followed a similar pattern. There was little difference in the sequence of presentation, form of classroom organization and classroom discourse patterns. The sequence of presentation generally followed the pattern that can be described as ‘teacher-led class discussion using situations and examples, followed by pupils’ examples and exercises. The failure of the teachers to use structured teaching materials and practical and game activities, and to rely solely on textbook routine tasks, indicate that the few who attempt to teach for conceptual understanding and application rely mainly on exposition and teach for reception and not discovery learning.
Source : Kofi Mereku methods in Ghanaian primary Mathematics textbooks and teachers classroom practice in Williams, J. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 23(2) June 2003.
Teaching is overly based on textbooks. As a consequence, children tend to fail items that deviate from the textbooks content or format.
Another author found that Mathematics teachers act before a passive audience that is supposed to absorb the knowledge transmitted. Usually when students do not understand a teacher’s method of presenting a mathematical concept, the teacher would not change the method of presentation. Instead, the teacher would blame the students for being lazy or unintelligent. Mathematics teachers are mostly interested in answers or solutions to mathematical questions or problems rather than the processes or methods used to obtain the answers or solutions. Mathematical concepts are taught as objective, discrete facts without linking them together. Students are hardly encouraged to ask questions, make comments or suggestions about what is being taught. Mathematics teaching is decontextualized.
Teachers hardly connect mathematical concepts that they are teaching to the lives of their students or cultural practices in our society. Examinations or tests are the only instrument for assessing students understanding of mathematical concepts. Scarcely do Mathematics teachers include class or homework assignments as a part of the weighing of the final marks. Mathematics is taught without using any other materials except chalk and chalkboard. Mathematics teachers have a hidden assumption that only the most brilliant students are capable of learning Mathematics. Some students are made to recite the multiplication table in a parrot-like fashion in the belief that once mastered it would facilitate the learning of other mathematical concepts.
Challenges and opportunities
The national syllabus is currently being revised to overcome these problems, and so should be teachers’ training. The changes should occur in the way teachers deliver lessons.
Recent research findings from Mathematics education show that integrating of ICT changes the nature of teaching and learning. ICT seems to provide a focal point which encourages interaction between learners and the technology itself. This implies that ICT used in instruction support constructivist pedagogy, where learners use technology to explore and reach an understanding of Mathematical concepts. Teachers must adapt to new roles.
To go further : Akyeampong K. (2017), Teachers educators practice and vision of good teaching in teacher education reform context in Ghana, Educational researcher, Vol. 46, May 2017, pp 194-203, AERA.
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