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. Contact information. [email protected] 22 85 48 77. Today’s and next week’s lectures.

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Sne4210 arithmetic acquisition and barriers teaching and learning 10 04 07

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

Guri A. Nortvedt


Contact information
Contact information

  • [email protected]

  • 22 85 48 77


Today s and next week s lectures
Today’s and next week’s lectures

  • 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!”


What is the role of learning in teaching
What is the role of learning in teaching?

  • Teaching = learning

  • Teaching learning

  • Teaching learning


Traditional teaching
“Traditional teaching”

  • 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


The case of norway solli 2004 traditional special needs teaching in mathematics
The case of Norway …(Solli, 2004)Traditional special needs teaching in mathematics:

  • 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


The case of norway teacher s and teacher student s reluctance to teaching mathematics
The case of Norway – teacher’s and teacher student’s reluctance to teaching mathematics

  • 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”


Young children
Young children reluctance to teaching mathematics

  • 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)


Core questions
Core questions reluctance to teaching mathematics

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?


Mathematical competency one model mogens niss 2002
Mathematical competency reluctance to teaching mathematics– one model – Mogens Niss (2002)

… 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)


Components of mathematical competency
Components of mathematical competency: reluctance to teaching mathematics


We are not really addressing mathematics only arithmetic
We reluctance to teaching mathematics are not really addressing mathematics – only arithmetic

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


An example 15 3
An example: 15 + 3 reluctance to teaching mathematics

  • Representations:symbol, concrete, tallies/ drawings/ fingers

  • Problems solving or fact retrieval or standard algorithm or….

  • Language- sum – addend – add…


Number sense example 1 griffin 2003
Number sense – example 1 reluctance to teaching mathematics(Griffin, 2003)

  • 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?


Three teacher orientations towards teaching numeracy
Three teacher orientations towards teaching numeracy reluctance to teaching mathematics

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

  • Transmission

  • Discovery

  • Connectionist


Important message from askew et al
Important message from Askew et al reluctance to teaching mathematics

  • What teachers say and what they do!

  • Found in other research projects –


The nctm vision standards 2000 the national council for teachers of mathematics
The NCTM vision (Standards, 2000) reluctance to teaching mathematics(The National Council for Teachers of Mathematics)

  • 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)


What then should teachers do
What then should teachers do? reluctance to teaching mathematics


A counting example fuson 1991
A counting example (Fuson, 1991) reluctance to teaching mathematics

  • 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


54 2 national tests project norway nortvedt unpublished
54 : 2 = reluctance to teaching mathematics(National tests project – Norway – Nortvedt, unpublished)

  • 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 boards
Hundred boards reluctance to teaching mathematics

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


Counting
Counting reluctance to teaching mathematics

  • 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?


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