Presentation on theme: "Mental Paper carried 20% of the global mark 20 questions 15 minutes long was recorded Written Paper carried 80% of the global mark 16 questions 1 hour."— Presentation transcript:
Mental Paper carried 20% of the global mark 20 questions 15 minutes long was recorded Written Paper carried 80% of the global mark 16 questions 1 hour 30 minutes long Number & Algebra - 30% ± 2% Measures, Shape & Space - 30% ± 2% Data Handling - 5% ± 2% Problem Solving - 35% ± 2%
The Mental Paper The Mental Paper was well-balanced and the level of difficulty was adequate. Consequently it was tackled successfully by the majority of candidates. Questions were meant to be worked out mentally but candidates were given the possibility to jot down working on the answer sheet for which they were not penalised. A number of schools reported that some students encountered difficulties in the Mental Paper due to the fact that it was recorded rather than read by the teacher. Amongst the comments was that not all the questions were clearly read and others noted that the words written in bold were not emphasised in the voice-over.
Strand: Number and Algebra Difficulty: Low to Medium The majority of the answers to this set of questions were correct. The part which led to most incorrect answers was (d) with 50 given as the answer.
Recommendation: Procedures (knowledge of rules and procedures used in carrying out routine mathematical tasks and the symbols used to represent mathematics) should never be learned in the absence of a concept (logical relationships, representations, using manipulatives, an understanding and ability to talk, write and give examples of these relationships).
Strand: Number and Algebra Difficulty: Low to Medium Students who managed to get the second answer, finished off the question correctly, but some children had 435 as their second answer, so they kept on working with it and therefore the rest of the answers were incorrect.
Strand: Number and Algebra Difficulty: Low to Medium Recommendation: It is of utmost importance to encourage students to be careful about checking their work, and to help them to develop a repertoire of checking strategies.
Strand: Shape and Space Difficulty: Low to Medium Most students answered this question correctly.
Strand: Shape and Space Difficulty: Low The vast majority of students answered this question correctly. Some confused the first net (and marked it) and the last net (and did not mark it).
Strand: Number and Algebra Difficulty: Low to Medium The students who did not get full marks in this questions mostly encountered difficulties in converting from fraction to decimal i.e. they converted to 3·5 rather than 0·6.
Strand: Number and Algebra Difficulty: Low to Medium This question did not pose any particular difficulties to most of the students.
Strand: Number and Algebra Difficulty: Low to Medium In this question, parts (c) and (e) turned out to be the most challenging. Common incorrect answers given in part (c) were 1·15 and 11·5 to the calculation 2·3 × 50.
Strand: Number and Algebra Difficulty: Medium Some students encountered difficulty in identifying the pattern in this question and a few others did realise that there was a gap in the table between shape number 5 and shape number 9.
Strand: Measures Difficulty: Medium The answers to Questions 9 (ai) and (aii) were correct in most of the scripts.
Strand: Measures Difficulty: Medium to High Less correct answers were seen in part (bi) and even less in part (bii). Many students had difficulty in converting from cm to mm. Other students multiplied 12·6 by 3, taking 12·6 cm for the length of the pencil.
Strand: Measures Difficulty: Medium to High No particular difficulty in this question was reported.
Strand: Number and Algebra Difficulty: Medium to High
The major difficulty in this question was encountered in part (b), where the students subtracted the percentage and not the amount of votes.
Strand: Data Handling Difficulty: Medium
This question did not pose any particular difficulty, except for part (e). A number of those students who gave a wrong answer did not value the picture of each burger in the pictograph as 6 burgers, as described in the key.
Strand: Data Handling Difficulty: Medium The answers to parts (a) and (bi) were correct in many cases. However, in part (a) the most common mistake was adding up all the weights to work out the average, without dividing.
Strand: Data Handling Difficulty: Medium to High Part (bii) was the most challenging.
Strand: Measures Difficulty: Medium
Difficulties were mostly evident in part (bii). Many students who got a wrong answer either started off with the incorrect time or computed the addition incorrectly. A common mistake was that 20 minutes to 4 was not written as 3.40 but either are 3.20 or 4.40.
Strand: Measures Difficulty: Medium Recommendation: Use of timeline.
Strand: Measures Difficulty: Medium to High
Common incorrect answers in part (a) i.e. in computing the area of the fish pond (90 cm × 90 cm) were 180 cm 2 or 810 cm 2.
Strand: Measures Difficulty: High The markers noted that it was rather difficult to assess valid attempts of students in part (a).
Strand: Measures Difficulty: High In part (b) a substantial number of students took the most obvious answers which was the direct route (9·7 km), without doing any working. However, the direct route is not necessarily the shortest route. So the students lost all marks in this case. Other common incorrect answers given were random distances from the table random working leading to different answers.
Recommendations Non-routine mathematical challenges and investigations should be encouraged. Closed routine problems, which follow a well-known pattern of solution, develop only a limited range of skills. These problems encourage memorisation of routine methods rather than experimentation and investigation. Without diminishing the importance of being fluent with basic techniques, routine methods only become useful tools when children can successfully apply them to non-routine and realistic problems. Understanding is a more robust outcome than just recall. A balanced mathematical programme of work incorporates concept learning and the development, maintenance and application of skills. These should be taught in such a way that students develop their ability to think mathematically.
Recommendations During the mathematics lesson students should be given the possibility to experience various situations and opportunities.
Recommendations Giving students both an opportunity to discover and invent new knowledge and an opportunity to practise what they have learned improves student achievement. Teaching that incorporates students’ intuitive solution methods can increase student learning, especially when combined with opportunities for student interaction and discussion. Students should be given ample opportunity to understand where each topic leads to mathematically. Connections that draw together key ideas and topics within and across strands help students develop a deeper, more coherent understanding of the concept or process they are learning. Students should be given the opportunity to try to understand their own errors. The most powerful learning experiences often result from making mistakes.
Recommendations Educators are encouraged to develop a shared language to describe teaching. This facilitates generation and dissemination of professional knowledge. Curriculum Development Sessions and Professional Development Sessions can be an opportunity for this to be done. Opportunities for using mathematics at other times of the day apart from the daily mathematics lesson should be sought. Educators are encouraged to learn more about learning difficulties that affect the learning of mathematics such as Dyscalculia in order to support students who are encountering difficulties better.
Please check out primarymaths.skola.edu.mt The Revised Primary Mathematics Syllabus Primary Maths Room on Fronter