mathematics knowledge. This knowledge is on skills and step-by-step procedures without explicit reference to mathematical ideas. Students committing procedural errors do not have an understanding of why or how procedure works; and do not recognize the importance of applying, and computing the procedure correctly (Elbrink, 2008). Conceptual errors result from lack or poor understanding of conceptual mathematical knowledge. Hope (2006) refers conceptual mathematics understanding as a knowledge that involves clear and systematic understanding of fundamental basic points behind the algorithms performed in mathematics. As Hull and Miles (2010) argue, students demonstrate conceptual understanding in mathematics when they provide evidence that they can generate examples of concepts; use and interrelate varied representations of concepts; identify and apply principles; know and apply facts and definitions; and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding also allows a student to apply and possibly adapt some acquired mathematical ideas to new situations. Thus, to avoid procedural and conceptual errors in mathematics, both procedural and conceptual learning are necessary with a consideration that, procedural learning needs to be coupled to conceptual learning and to real-life applications. When students make some generalizations which are not correct, they create misconceptions. A misconception is not wrong thinking. Instead, it stands as a premature concept or a local generalization that the student has made. Thus, it is very difficult to avoid misconceptions during learning since are formed when students systematically use incorrect rules, or use correct rules beyond their proper
mathematics knowledge. This knowledge is on skills and step-by-step procedures without explicit reference to mathematical ideas. Students committing procedural errors do not have an understanding of why or how procedure works; and do not recognize the importance of applying, and computing the procedure correctly (Elbrink, 2008). Conceptual errors result from lack or poor understanding of conceptual mathematical knowledge. Hope (2006) refers conceptual mathematics understanding as a knowledge that involves clear and systematic understanding of fundamental basic points behind the algorithms performed in mathematics. As Hull and Miles (2010) argue, students demonstrate conceptual understanding in mathematics when they provide evidence that they can generate examples of concepts; use and interrelate varied representations of concepts; identify and apply principles; know and apply facts and definitions; and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding also allows a student to apply and possibly adapt some acquired mathematical ideas to new situations. Thus, to avoid procedural and conceptual errors in mathematics, both procedural and conceptual learning are necessary with a consideration that, procedural learning needs to be coupled to conceptual learning and to real-life applications. When students make some generalizations which are not correct, they create misconceptions. A misconception is not wrong thinking. Instead, it stands as a premature concept or a local generalization that the student has made. Thus, it is very difficult to avoid misconceptions during learning since are formed when students systematically use incorrect rules, or use correct rules beyond their proper
Victor_Mwesiga_%2D_PhD.docx