Chapter Eighteen - Additional Resources

Observational field notes on assessment situations

27 February 2003
Class: Form Four students
Lesson: Mathematics
Time: 9.50 – 11.10
Topic: Pythagoras’s theorem
Number of students: 50

Seating: the teacher is at the front of a class which is set out in rows of single desks.

Equipment: pencils, rulers, compasses, centimetre-squared paper, whiteboard.

9.50: teacher arrives in the class

9.55: class settles, all the books are ready and the class is quiet. The teacher distributes centimetre-squared paper, one to each student, and instructs them to write their name on them. The teacher checks that everyone has a ruler and pencil.

10.00: The teacher tells the class that they are going to be finding out some properties of a particular kind of triangle, a right-angled triangle and that they are doing to do this by some simple measuring and counting activity.

10.02: The teacher tells the students to go to the middle of their squared paper, and rule a pencilled line 3 cm long, vertically. She shows the students how to do this on the whiteboard. The students do this, and the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct.

10.04: The teacher reminds the students of the work they have done previously on right angles, using the phrase a ‘square corner’ to explain the concept. She asks the students to rule a pencilled a line 4 cm long, at right angles (i.e. horizontally), starting at the bottom of the first line and going in the direction of the right hand side of the page. She shows this on the whilteboard. The students do this, and again the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct.

10.06: The teacher asks the students to make the third line of the triangle by joining up the two other sides, showing them on the whiteboard how to do this, and, as before, checking that they have done this. She asks the students to measure the length of this line, and she confirms with them that it is 5 cm long.

10.12: The teacher questions the students to recall what is meant by the hypotenuse, indicating on the whiteboard diagram the right angle and the fact that the hypotenuse is opposite to it. She asks the students to construct a square using the 3 cm line as one side, and constructing that square to the left hand side of the page. As before, the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct.

10.14: She asks the students to construct a square using the 4 cm line as one side, and constructing that square to the bottom edge of the page. As before, the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct.

10.16: She draws on the whiteboard the square on the hypotenuse, and asks the students to do this on their page. As before, the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct.

10.18: She asks the students to calculate the area of the square that they have just drawn (5 x 5 = 25 square cms), reminding them how to calculate the area of the square.

10.20: She asks the students to count the number of squares for the area of the 3x3 square, the number of squares for the 4x4 square, and to add them together (= 25 square cms). She asks the students what they notice about the sum of these two squares and the area of the square on the hypotenuse (they are the same).

10.23: She asks the students to tell her the ‘rule’ that they have discovered, in words. Many students want to volunteer. The teacher chooses some students whom she thinks will not have it quite correct; some students give her an incorrect answer, and she asks the class why the answer is incorrect and what needs to be done to correct it. The class agrees a ‘rule’ or ‘formula’ which she writes on the whiteboard.

10.30: five minute break

10.35: The teacher reminds the class of how to construct a triangle with the length of each side given (work from a previous lesson). The students construct a triangle of sides 5, 6, 7 cms. As before, the teacher quickly moves round the class to check that they have all done this correctly, and she helps those in difficulty (e.g. those who started at the wrong place on the page). She carries an eraser with her, explaining to those in difficulty what they were doing wrong and what to correct. Several students have problems with this, so she stops the whole class to remind them of the rules for constructing triangles, and then gives more time for them to complete it. Some students lean over their desks to help each other.

10.45: The teacher asks the students to calculate the areas of the squares of each side, and asks them if the rule applies. The students note that it does not as the triangle is not a right angled triangle, so the initial formula has to be revised to ensure that the rule mentions a right-angled triangle. The students write down the final, correct version of the formula.

10.55: The teacher asks the students to suggest where the rule that they have learnt might be applied in everyday life.

11.00: The teacher quickly performs the same activity on a triangle of sides 6, 8, 10 cms, to draw attention to the issue of proportionality of the length of the sides. She then sets the homework for the class: (a) to draw three right angled triangles and calculate the area of all three sides when the length of only two of them are known; (b) to list five ways oin which the rule can be applied in real life.

11.10: Lesson ends