Teach-Primary-Issue-19.7

John Tomsett is a former teacher and head with over 33 years of experience. He is also an education consultant, and the author of 13 books, including Love Over Fear: Creating a Culture for Truly Great Teaching and Mind Over Matter: Improving Mental Health in Our Schools . She began by writing the question on the board: 1/4 + 1/5. A strict 3-2-1 SHOW! revealed two answers… 2/9 and 9/20. She invited a pupil to explain how he came to the answer 2/9. He described adding numerators and then the denominators. In superb children’s entertainer mode, she feigned amazement and declared that sounded right to her. She then asked another pupil how they ended up with 9/20, and responded positively to that answer, too. Seemingly confused – “Goodness me! Both those answers sound right…” – she gave the pupils time to think about the two answers, 2/9 and 9/20. She then asked them, in pairs, to decide whether the correct answer was 2/9 or 9/20, and, a minute later, every single pair had written 9/20 on their boards. She had bellwether pupils in the room and probed their reasoning, safe in the knowledge that if they could explain how to arrive at the right answer, it was likely all the pupils would be able to. Rethinking planning Let’s think about 1/4 + 1/5 in more depth. Determining how many potential answers might arise will help you anticipate pupils’ misconceptions. Consequently, your planning time can be spent preparing clear explanations, so that your pupils understand their misconceptions and adopt the correct mathematical thinking to arrive at the right answer. Here are 10 possible (but incorrect) answers to 1/4 + 1/5. I have explained the misconceptions for the first two. To prepare thoroughly for teaching 1/4 + 1/5, you should think about the implicit misconceptions behind all the incorrect answers and how you would explain each so that children don’t make the same mistake in their mathematical thinking in the future. This is the best preparation for adaptive teaching. I will leave the explanations for misconceptions 3-10 up to you! 1. 9/40: The pupil correctly finds the common denominator as 20 and converts the fractions to 5/20 and 4/20. However, instead of only adding the numerators and keeping the denominator as 20, they incorrectly add the denominators as well. 2. 11/45: The pupil simply combines the numerators to make 11, and combines the denominators to make 45. 3. 2/20: 4. 11/9: 5. 2/45: 6. 11/20: 7. 1/20: 8. 1/40: 9. 0.45: 10. 11/40 No matter how many misconceived answers you anticipate, there will always be one that catches you out, because children’s minds are fascinatingly unpredictable! She then asked them to discuss in the same pairs why someone might have written 2/9. What she made sure not to do, was humiliate the pupil who had written 2/9 first time round. The success of this teacher’s approach derives from her taking the time in her planning to anticipate the main misconceptions and to have an adaptive plan for disabusing the pupils of each misconception. If they had all written 2/9 on their whiteboards, she was ready to reteach how to add fractions with different denominators. The teacher said to me, “I’m working hard on addressing the pupils’ mathematical misconceptions there and then, in the lesson. I’m trying to be more proactive in getting them thinking about how to improve their work in the moment, and giving oral feedback, having anticipated their possible errors.” TP johntomsett.com Teacher on the visualiser TA on the whiteboard Step 1: 3 3/8 + 6/8 = Step 2: 3 3/8 + 6/8 = 3 Step 3: 3/8 + 6/8 = 9/8 1 + 1/8 Step 4: = 3 + 1 1/8 Step 5: = 4 1/8 Fig. 1 www.teachwire.net | 59 MA THS S P E C I A L 1. Are the denominators the same? If yes, no change; if no, use LCD. 2. Carry the whole number across the = sign. 3. Add the fractions together: add numerators/ common denominator. Is the sum an improper fraction? If so, make it a mixed number… Youmay need to use the part/whole model. 4. Add the whole number and the mixed number together. 5.Write down your final answer.