Week 8 -Objective 1

1. Objective 1 – Know and be able to use a selection of standard and other written methods for calculating. Standard algorithms are not easily grasped by children because they do not correspond with how most children naturally think about numbers (Anghileri, 2000, p. 89). Without understanding children may make errors reconstructing procedures and follow the wrong rules (Anghileri, 2000, p. 92). Therefore children at first should use their own mental algorithms to solve problems before learning more efficient written methods (Anghileri, 2000, p. 109). Children must be actively involved in constructing their own mathematical learning and must choose a method of calculation that suits each mathematical setting and is easy for them to understand (Reys et al., 2009, p. 239). The success rate is higher when children invent non-standard algorithms alongside school taught algorithms (Anghileri, 2000, p. 90).

2. A wide variety of non-traditional strategies are used by children to calculate algorithms (Reys et al., 2009, p. 236) such as: - Traditional vertical two digit subtraction where the child subtracts ones first then the tens (Reys et al., 2009, p. 236). - Partial-sum addition or subtraction or multiplication – children can work in any order left to right, right to left or out of order. It is similar to a standard algorithm and a good transitional algorithm for eventually learning the more efficient standard algorithm (Reys et al., 2009, p. 243). - A hundreds board is used for subtraction where a child starts at the larger number and counts back by ones to the smaller number(Reys et al., 2009, p. 236). - 27 plus how many is 56 (Reys et al., 2009, p. 236). - Draw 56 single circles and put a cross through 27 and count those not crossed (Reys et al., 2009, p. 236). - Horizontal number sentences and separate ones from tens. For example: 56-27 - start with tens and subtract 50-20 =30. Then subtract 30-7 = 23, then add 23+6 = 29 (Reys et al., 2009, p. 237). - Some children work from left to right - 56-27= 56-20= 36 36-7=29 (Reys et al, 2009, p. 237). Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). Helping children learn mathematics (9thedition). New York: John Wiley & Sons. Anghileri, J. (2000). Teaching number sense. London: Continuum. (Chapter 6).