2. PROBLEM AREAS IN MATHEMATICS EDUCATION By C.K. Chamasese

3. Rationale Studies have shown that lack of numeracy was related to unemployment and low income among the adults. Generally results are very poor in mathematics especially at school certificate level.

4. Mathematics is commonly seen as one of the most difficult subjects by students and adults alike. Mathematics is a prime vehicle for developing childrens’logical thinking and higher – order cognitive skills Mathematics is also a crucial component of other scientific fields such as physics, engineering etc.

5. ln order to design and develop learning environments that promote understanding efficiently, teachers need to be aware of students’ difficulties in learning mathematics..

6. Cognitive research has shown that some students at risk for mathematics failure have not developed a sufficient conceptual foundation in number sense and mathematics operations. The hierarchy of mathematics requires that students develop a strong mathematical foundation to ensure their future success.

7. What then are the problem areas in Mathematics Education? 1. Mathematical misconceptions Students are often found to have misconceptions about mathematics which impede their learning of the subject. It is important for teachers to address these from the start.

8. Addressing misconceptions can improve students’ mathematical achievement Misconceptions occur when a rule is over generalized to situations in which it is not applicable. e.g 1. Rule : when multiplying a number by powers of 10 adds a zero at the end. They then generalize to when multiplying decimals 5.8 X 10 = 5.80 (incorrect) e.g. 2. Rule: Multiplication always makes things bigger, division always makes things smaller. 2 X 6 = 12 (bigger) but ½ X 6 = 3(smaller)

9. Remedies Let pupils explain how they come up with their answer whether right or wrong. Correct the Wrong answer immediately. Teachers should also provide detailed justifications of the solutions they are using. Students benefit more when teachers encourage them to share their thinking process and justify their answers out loud or in writing as they perform mathematics operations

10. Teach the exact meaning of mathematical terms right from the start as it is more difficult to unlearn inexact mathematical meaning they have internalized. It is more effective to let students make the mistake first and then to discuss afterwards, rather than giving students examples of misconceptions before hand.

11. 2. Abstract nature of mathematics Abstract nature of mathematics often causes problems to both pupils’ learning and their attitudes towards mathematics. Difficulties to link mathematics learnt in classroom to real life situations. In most cases a problem set is introduced, followed by a solution technique,then practice problems are repeated until mastery is achieved. Additionally, it is taught as if there is a right way to solve and any other approaches are wrong.

12. Remedies Using real life contexts e.g 1. integers: (a) John was born in 1982, how old was he in (i).1991 (ii) 1972 1972 1982 1991 (b) points lost in a game (Negative), points won in a game (Positive). (c) temperatures above freezing point (positive) and temperatures below freezing points (negative). -20⁰ -15 ⁰ -10 ⁰ -5 ⁰ 0 ⁰ 5 ⁰ 10 ⁰ 15 ⁰ 20 ⁰

13. 3. Difficulties in making connections Learners are unable to make connections between the mathematics knowledge they possess and what they learn at school. e.g Sets Ask the learners about how sets are used on a market stand. Learners will be in a position to explain how sets are used on a market stand and this will make them see the sense in the topic which will in turn enhance their understanding of the topic.

14. 4. Difficulties in learning written symbols Standard written symbols play an important role in student learning of mathematics, but students may experience difficulties in constructing mathematical meaning of symbols. Students derive the meaning of symbols from either connecting with other forms of representations or establishing connections within the symbols systems. Students might have difficulties in understanding the meaning of a written symbol if the referents do not well represent the mathematical meaning or if the connection between the referent and the written symbol is not appropriate.

15. For example, the symbol a/b can mean a relationship between two quantities in terms of the ratio interpretation of rational numbers. Similarly, it is also used to refer to an operation. For this reason teachers need to use other types of representations like sets of discreet objects and the number line to promote conceptual understanding of the symbol.

16. Most of the difficulties in understanding symbols comes from the fact that in their standard form, written symbols might take on different meaning in different settings. For instance, in solving the equation 2x + 3 = 4, x is an unknown which does not vary, whereas it varies depending on y in the equation 2x + 3 = y.

17. In order to understand mathematical symbols, students need to learn multiple meanings of the symbols depending on the given problem context. Therefore, they should be provided with a variety of appropriate materials that represent the written mathematical symbols, and they should also be aware of the meaning of mathematical symbols in different problem contexts.

18. 5.Overgeneralized rules and procedures Student errors are often systematic and rule based rather than random. These errors may be caused by instruction that focuses on rote memorization. When students’ knowledge is rote or insufficient, they might over generalize the rules and procedures. For example, students might over generalize the rule for subtracting smaller from larger if they are only taught to subtract the smaller from the larger number.

19. Remedies One way to reduce such difficulties is to help students make connections between conceptual knowledge and procedural knowledge. The construction of conceptual knowledge requires identifying the characteristics of concepts recognizing the similarities and differences among concepts according to these characteristics and constructing the relationships among them.

20. 6. Using inappropriate representation Teachers need to design instruction that helps students construct big ideas. For example, student having difficulty in adding fractions may extrapolate erroneous algorithms from instruction on the representation of fractions.

21. Conclusion Developing understanding in mathematics is an important but difficult goal. Being aware of student difficulties and the sources of the difficulties and designing instruction to diminish them, are important steps in achieving this goal. Student difficulties in learning written symbols, concepts and procedures can be reduced by creating learning environments that help students. Build connections between their formal and informal mathematical knowledge..

22. Using appropriate representations depending on the given problem context. Helping them connect procedural and conceptual knowledge. With the awareness that mathematics understanding is actively constructed by each learner, we can intervene in this process to advocate for or provide experience with manipulative skills,time for exploration, discussions where the right answer is irrelevant, careful and accurate language, access to helpful technologies and understanding.

23. THANK YOU FOR YOUR ATTENTION