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SNE4210 - Arithmetic acquisition and barriers: Teaching and learning (10.04.07)

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SNE4210 - Arithmetic acquisition and barriers:Teaching and learning (10.04.07)

Guri A. Nortvedt

- [email protected]
- 22 85 48 77

- Outside and in:- raise some questions to think about: about mathematics teaching and learning- something about the present state- good general principles- some examples from special education“Everybody knows what it means to KNOW mathematics, but there is no consensus on how to TEACH mathematics!”

- Teaching = learning
- Teaching learning
- Teachinglearning

- Believing knowledge can be transferred from one person to another
- Students seen as empty boxes – to be filled
- Telling or explaining
- Black board
- Text books
- Independent work
- Silent work

- Inclusive schools
- Norwegian students really like their schools
- 0,4 % in special needs schools
- 5,5 % of the students
- Gender difference: 70 % boys – 30 % girls
- Late
- Not as successful as wanted
- Traditionally – one teacher – one student
- Doing over and over again
- The same procedure as last year
- Fragmenting and isolating knowledge

- I can do it if you tell me the formulae, but I do not understand why it works….
- Mathematics viewed as instrumental
- I prefer not to….
- Many teachers lack formal training
- An official view? “If you teach young children you need less formal training that if you teach secondary school children”

- Comes to school eager to learn to read and do mathematics
- Already have much knowledge and competencies:- can count- simple sums and subtractions- can compare- can describe- can sort- have an understanding for time and space(- have a language)
- The squirrel task – a division problem: (1 squirrel mom, 3 squirrel children and 13 nuts)(Alseth, 2003)

1. What is mathematical competency?

- Mathematics for all
- Skills for life long learning
- Back to basics movements
2. How can mathematics be thought?

3. What obstacles in learning mathematics should teaching be sensitive towards?

… to be mathematically competent is to be prepared to act with consciousness and insight in situations containing a specific kind of (mathematical) challenges

* To be able to pose and answer questions in, with and about mathematics

- To be able to use the mathematical language and tools
- (http://pub.uvm.dk/2002/kom/) (full report – but in Danish, so not for all of you)

- Think about it– in this model – what does arithmetic consist of?

- Representations:symbol, concrete, tallies/ drawings/ fingers
- Problems solving or fact retrieval or standard algorithm or….
- Language- sum – addend – add…

- Can you see 3/5 of something?
- Can you see 5/3 of something?
- Can you see 3/5 of 5/3?
- Can you see 2/3 of 3/5?
- Can you see 1 + 3/5?

- Askew et al (King’s College) (1997, 2000, 2001):- What characterizes effective teaching?- Who is at the centre? Responsibilities? Roles?
- Transmission
- Discovery
- Connectionist

- What teachers say and what they do!
- Found in other research projects –

- Constructivism is a theory about knowledge and learning; it describes both what “knowing” is and how one “comes to know”. Based on work in psychology, philosophy, and anthropology, the theory describes knowledge as temporary, developmental, monoobjective, internally constructed, and socially and culturally mediated. Learning from this perspective is viewed as a self-regulatory process of struggling with the conflict between existing personal models of the world and discrepant new insights, constructing new representations and models of reality as a human meaning-making venture with culturally developed tools and symbols, and further negotiating such meaning through cooperative social activity, discource, and debate. (Fosnot, 1996)

- String level
- Unbreakable list level
- Breakable chain level
- Numerable chain level
- Bidirectional chain level
Donlan and Hutt (1991)

- Susie – age 8
- Wants to learn to count to 100

- Grade 4 student – girl
- 54 : 2 =
- Divides worksheet in two – makes a tally on left hand side – right hand side – left hand side – a total of 54 times
- Counts each side – gets totals of 27 on both sides
- Concludes – 54 : 2 = 27

- (hundred board on over head projector to illustrate patterns and regularities, different strategy use among participants…)

- For next weeks lecture, I would like you to think about how teachers in your country views counting in the mathematics classroom. What would a teacher do if a student use counting to solve a mathematics problem?