# Overthinking?

Discussion in 'Mathematics' started by casperyc, Mar 21, 2016.

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## Is this question over complicating the use of pythagoras?

3 vote(s)
27.3%
2. ### No, it's NOT over complicating it.

8 vote(s)
72.7%
1.  Here is a question from the NEW 9-1 SAM with its mark scheme.

Am I being too simple or the mark scheme is just making it "too complicated"?

Reason: Really simple question, here is a SQUARE ABCE (told in the question). To find its area, ALL we need to know is the LENGTH of its side. So using pythagoras, it's sqrt(x^2+y^2). Hence the area of ABCD is x^2+y^2.

WHY does the mark scheme gives such a complicated method??? The way it's done it is to PROVE pythagoras. But the question is testing HOW TO USE pythagoras.

What do you think?

2. Your method is in the mark scheme in the second C1 mark. so the students get the first C1 for an attempt to do something with algebra and area of shapes, the second for showing either that they intend to subtract the area of the triangles form the area of the square OR for calculating the length of the hypotenuse and squaring. The final C1 is for doing everything correctly and finishing with the original expression for the area.

These mark schemes are illustrative of expected solutions, but in problem solving questions, there are numerous ways in which students may attempt the question, many of which will be discussed by examiners during the marking process, all valid methods will gain marks.

In SAMs materials, the awarding organisations offer some likely model solutions, in live assessment, if a large proportion of students attempted the question in a different way to what was anticipated, it is likely that this new method would also be detailed as an alternative solution in published mark schemes following results day.

The SAMs are developed to demonstrate to Ofqual what the ao's approach is and to illustrate to teachers what the look and feel of the new papers are, they are not meant to be thought of in quite the same way as "live" assessment. The mark schemes have not gone through the semi-iterative process that happens when confronted with several hundred thousand student responses.

colinbillett and wanet like this.
3. The mark scheme has given two options, one of which is the one you describe. It would not be fair to penalise students for taking an alternative, but perfectly effective, approach.

4. We simply have to accept that many learners will not see what the OP sees, and will proceed as the mark schemes suggests. They don't get penalised for this, appropriately so, but may not be up to the algebra to complete the solution. What the OP sees as 'complicated' is the natural first step for many, if not most, of the learners who will attempt this question.

5. I am generally very picky on the use of mathematical reasoning and proofs (as I was taught until secondary level in Shanghai (China). So bear with me a second if you can.

I am not saying that we should "penalise" any answer. Simply, I am not quite sure if the "long answer" should be used here, as it is NOT very appropriate at this secondary level (at least not in UK, I think).  Reading this question carefully, it tells you that ABCD is a square.

It DOES not tell you the the big shape is a square.
So YOU NEED TO PROVE EFGH IS A SQUARE as a first step!

Not being disrespectful, how many students can prove this in UK?
You need to show that EAF is on a straight line (or similarly)

In the mark scheme, it only says "start chain of reasoning ........area of large square......". Who said the large quadrilateral is a square here?

If we want students to learn good mathematics, I have to say this question is a negative example of it. It has no logical thinking.

And the funny thing is, it is a question on "reasoning", when the mark scheme hardly shows any of it.

6. The second 'C1' mark uses this implication of the proof.
The [tex](x+y)^2[/tex] is the area of the bigger square. This has come about from their recognising each side of quadrilateral EFGH is of length x + y and then multiplying x + y by x + y.
The mark scheme would not write out this full method [i.e. (x+y)(x+y) = (x+y)^2 ] but most students attempting this question, and using this method and not the one stated by the OP would have it in their working somewhere.
It's an implicit bit of logical reasoning ... Now if it were to be one of those questions that stated "give reasons for your answer" that would be where they would have to explain why and where it came from.

7. Why go with a complicated solution when the simple one given by @casperyc is sufficient. It does not matter if the EFGH is a square or not. Each side of the square ABCD is the hypotenuse of the given triangle.

Is this testing mathematical thinking or are the examiners testing if the students have been taught a generic method for this type of problem, hence the overly complicated solution?

8. Last edited: Apr 18, 2016
9. I can't see how this is not over complicating it.

Or at least it is not testing the maths, but whether the student can get inside the mind of the person who set this question.

As a student I take one look at the diagram and wouldn't even work out the area of the big square first.

Last edited: Apr 19, 2016