ED1635 Lecture Notes - Lecture 1: Spoken Language, Number Sense, Zero Zero (Comics)
Mathematics - Lecture 10 - Week 10
Written Algorithms, Understanding Operations and Calculating - Part 2
Additive Property of Zero - Additive Identity
- Adding zero (0) to any number leaves it unchanged.
e.g. 456 + 0 = 456
2 395 + 0 = 2 395
Multiplicative Property of One - Multiplicative Identity
- Multiplying a number by one (1) leaves it unchanged.
e.g. 456 x 1 = 456 2 395 x 1 = 2 395
Multiplicative Property of Zero - Zero Property
- Multiplying a number by zero (0) gives an answer of zero.
e.g. 456 x 0 = 0
2 395 x 0 = 0
Developing Mental Strategies for 2 Digit Numbers
Importance of Automaticity in Mathematics
- Lack of math-fact retrieval can impede:
- math class discussions (Woodward & Baxter, 1997),
- Successful mathematics problem solving (Pelligrino & Goldman, 1987)
- the development of everyday life skills (Loveless, 2003).
- Rapid math fact retrieval has been shown to be a strong predictor of performance on mathematics
achievement tests (Royer, Tronsky, Chan, Jackson, & Marchant, 1999).
- Once procedures are automatised, they require little conscious effort to use, which, in turn, frees
attentional and working memory resources for use on other more important features of the problem
(Geary, 1995).
Drill and Practice Programs
- Drill and practice programs have demonstrated a positive effect on improving the retrieval speed for
facts already being recalled from memory (Woodward, 2006).
- However, drill and practice had no effect on developing automaticity for non-recalled facts
(Hasselbring, Goinn, & Sherwood, 1986).
Accuracy
- Usually involves careful recording and double-checking results
Efficiency
- Implies that the student does not get bogged down by adopting a procedure which is easily carried out
Flexibility
- Requires the knowledge of more than one approach to solving a problem, students need to be flexible
to be able to choose an appropriate strategy
Student Invented Strategies
- Any strategy other than a standard algorithm (therefore a mental computation strategy is a simply
an invented strategy that’s done mentally).
- There is mounting evidence that students both in and out off school can construct methods for adding and
subtracting multi- digit numbers without explicit instruction.
- Carpenter et al., 1998, p.4
Contrast with Standard Algorithms
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Written algorithms, understanding operations and calculating - part 2. Mathematics - lecture 10 - week 10 e. g. 456 + 0 = 456. 2 395 x 0 = 0 e. g. 456 x 1 = 456 2 395 x 1 = 2 395. Adding zero (0) to any number leaves it unchanged. Multiplying a number by one (1) leaves it unchanged. Multiplying a number by zero (0) gives an answer of zero. Rapid math fact retrieval has been shown to be a strong predictor of performance on mathematics math class discussions (woodward & baxter, 1997), Successful mathematics problem solving (pelligrino & goldman, 1987) the development of everyday life skills (loveless, 2003). achievement tests (royer, tronsky, chan, jackson, & marchant, 1999). Once procedures are automatised, they require little conscious effort to use, which, in turn, frees attentional and working memory resources for use on other more important features of the problem (geary, 1995).
