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Common Misconceptions and Error Patterns

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Common Misconceptions and Error Patterns

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Goal: Identify frequently made student errors or misconceptions based on the markers' report.

Which questions do you think our students will have the highest rates of incorrect answers?

What do you think will be their misconceptions?

Are these misconceptions aligned with patterns seen in our own classrooms?

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Goal: Evaluate how the question structure may have influenced student performance.

State the questions that seemed overly wordy, abstract, or context-heavy?

Which questions required higher-order thinking skills versus procedural fluency (i.e. the ability to accurately, efficiently, and flexibly carry out mathematical procedures).

How well do these question types align with our current teaching and assessment practices?

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Teaching Strategies and Intervention Ideas

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Teaching Strategies and Intervention Ideas

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Goal: Brainstorm actionable teaching strategies to address the challenges identified.

What teaching approaches might help prevent the common errors?

Are there specific skills or concepts we should reinforce more often or differently?

How can we adjust our formative assessments to better prepare our students?

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Common error in recalling of compound interest formula

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Common error in recalling of compound interest formula

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The frequent mistaking of A in the formula as interest instead of principal + interest commonly occurs in our students too. The mistake occurs because most likely they confused it with the format for simple interest formula where the Interest is the subject.

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Questions that seemed overly wordy, abstract, or context-heavy

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Questions that seemed overly wordy, abstract, or context-heavy

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Q8

Q13b

Q15

Q17b

Q19

Q21b

Q26

Q27b

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Common error pattern - change in sign when simplifying

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Common error pattern - change in sign when simplifying

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Q5

Change in sign when condensing especially the last 2 terms as a single fraction

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quite some of our students are similarly weak in algebraic manipulation, especially in the expansion of (a+b)^2 and (a-b)^2 where they frequently omit the middle term. Another common one is thinking that they can individually apply the square root when there are two separate terms within it. E.g. Square root of (x^2+y^2) becomes x+y.

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Common Error pattern - misreading of  values in a grid/number line especially for -ve values

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Common Error pattern - misreading of  values in a grid/number line especially for -ve values

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Q2/9

Some students tend to misread values (especially -ve values) in the number line/graphs

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At the sec 2 level when algebraic identities are introduced, especially for (a+b)^2 and (a-b)^2 , a worksheet that purposely writes in the wrong answers (for e.g. leaving out the middle term in expansion) can be used (in class/as hw) so that students can learn to view their own solutions from the markers perspective and get accustomed to spotting their own mistakes.

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Students may forget to account for the negative sign for the last algebraic term. As a result, they may tend to make mistake in the consolidation of terms which result in an early mistake.

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Qn 26b - application of different questions in the same question

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Qn 26b - application of different questions in the same question

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In a mensuration question, students need to use the concept of similarity of solid figures to find the appropriate length to use.

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The usual way of phrasing is "The bearing of D from B is 116 degrees." So this way of phrasing has confused some students whereby they instead thought of the bearing as from D instead and hence they got 244 as the answer.

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Common error pattern - accuracy of answer

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Common error pattern - accuracy of answer

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Q25

Students often focused on solving the quadratic equation, leaving their answer correct to 3 significant figures.

Did not read question carefully (which requires 3 decimal places, instead)

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The misreading of Q led to large number of students not getting the Q right as they mistook the number written in the Venn diagram as an element instead of the number of elements. The misreading of Q is not unique to this Q alone and is very rampant in our students too. Perhaps many jump to the diagram/main body part of Q instead of taking the time to really read the Q and to take note of the key points mentioned.

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Teachers will need to make a more concerted effort to help students see that a polygon question can include concepts on ratios. It is important for students to apply concepts from prior chapters to qns on another topic.

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Q12b Changing the subject, not putting +/-

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Q12b Changing the subject, not putting +/-

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Some students will forget to put +/- sign after taking square root.

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The word "greater than" presents an issue as most students will not read off from the top part of the graph but instead will read off from the bottom. Very common misconception

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Q24 Unable to recognise x^4-16 as difference of squares 

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Q24 Unable to recognise x^4-16 as difference of squares 

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Students tend to struggle with algebraic eqn/expressn with higher degree of the type in this question

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Reiterate concepts across different chapters

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Reiterate concepts across different chapters

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When going through more complicated questions, to ask students to identify the concepts they require to solve the question. This could help them recall prior knowledge of concepts and help them to appreciate that math concepts are not taught in silos.

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To tackle the issue with this Q, we can add an extra part to part (b) whereby in this new (c) we have an almost similar Q but this time round it is "less than" so that students can appreciate the difference between these two type of Qs.

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Questions on sets & Venn diagrams have become more complicated over the years, requiring students to identify a series of union/intersection of sets. Will need to teach our students how to analyse the given notation and use shading of sets to identify the correct area.