Have been tackling % word problems and these are some of the issues that surface :
Like to think for whatever number given in the question 100%
They are not really thinking about the question. Have tried to get them to use the 5Rs they had learning in the workshop (Read, Reflect, Recreate, Reduce, Revise) . Need to emphasize this over and over again. The next thing I am going to do is to get them to repeatedly always ask themselves : What represent 100%?
2. Solving for 1%
100% –> 200
1% —> 100/200
Trying to get them to see it by asking them : How you get to 1% (Divide by 100)? So, you have to do the similar operation with 200.
3. Inaccurate results
At the intermediate steps, they give their answer to 2 decimal place and use this answer to derive the final answer. The final answer may be inaccurate due to loss of accuracy in the intermediate steps. Remind them to always leave the answer as fraction in the intermediate steps
The progress has been slow but I do see some improvement in the students’ work. Through % problems, I am trying to get them in the habit of think more about the problem. Such habit is important as the students would generally just “whack any numbers they like”. To me, this is one of their most “potent” weakness which causes them to perform badly in Maths.
I have been using See Saw lately with my maths class.
Currently, I am using that to highlight students’ error and showcase students’ work. It is actually no much different from doing on their worked example book. Except that you can showcase your work publicly for your class to see. From my observation, it seems that pupils were more energized to do their work now. I also get to see the students’ work at one go and have some inkling where their gaps are.
How I am using SeeSaw:
Error Analysis – Show the student’s error and get them to see what is wrong
John has thrice as much money as Amy. The ratio of money of Amy to Zane is 3: 1. Zane has $16 lesser than John. How much does John have?
Here are some of the issues my pupils were having:
My pupil started off promisingly with this model–
With Zane coming into the picture, the model becomes like this
My pupils do know about ratio and thrice as much . But they get all mixed up when there is 3rd party . Why? They seem to assume that all units are the same.
To solve this misconception, I would need them constantly check their model back to the question. Guess I will emphasize that in my subsequent lessons.
2) Even if the model is correct, they have problem identifying the number of units representing 16. They seem to see the 16 and forget the lesser. I guess I will need them to highlight the words so that they can be constantly reminded.
I had used the Socrative App for the very first time in my Mathematics lessons. In this lesson, I set a few PSLE-style MCQ questions for the pupils to try.
What went well
Pupils were very enthusiastic (possibly the first time that they were using it) and eager to try the questions. The instant responses let me know what my students’ learning gaps were.
What comes after
Pupils were too over enthusiastic and might not be learning concepts when I was going through the answers with them. They just wish to try out the next question and see if they get it correct. They were “too high” during the lessons. This is not actually a bad thing as this will motivate them to do Maths.
However, to further deepen their understanding, I would need to reiterate to the pupils the purpose of the exercise. They need to learn from their mistakes and try not to make them the same mistake again. I cannot assume that they would just know the concept just because I had gone through with them. I would need to think about how I can create some meaningful learning experience so that they could grasp the concepts.
It has been two weeks since school reopens and of course, I have been teaching for the past two weeks. For this year, I have made a conscious efforts to get my pupils to reason out their working. I have been observing my pupils at action and found that they would just “anyhow” put the numbers together without much reasoning. In essence, they were not thinking about their working.
I had to stop myself from giving them the answers and “interrogated” them why they were doing that. Their answer were very vague and not precise. Currently , I am teaching them geometry and they would give reasons like “angles in a straight line” and ” angles in a triangle”. I pushed them further and wanted them to tell me the exact straight line and the triangle.
It has been two weeks and I hope that my pupils could slowly pick out this habit. And , I must also stay strong and should resist the temptation to go back to the “old way” (e.g., dishing out of the answers due to “time no enough”). I would go for less now so that my pupils can have more in the future.