Using an ILS to support learning of numeracy and basic algebra

Teresa FarranLecturer ICT & Mathematics Education

Using an ILS to support learning of

numeracy and basic algebra


“There is unprecedented concern .. in higher education about the mathematical preparedness of new undergraduates”

London Mathematical Society(1995)

• Post Dearing – Government agenda to widen participation– Recommending the use of IT in teaching and learning in HE

• 4/98 QTS requirements

Background


Considerations• Limited research maths requirements & needs

within HE – Similarity to KS3 and 4 common errors and

misconceptions?– Relevance of GCSE attainment?

• How to provide good educational opportunities for those with low motivation in learning mathematics

• Effectiveness of using CBL in mathematics • Products available


Questions posed

Do common errors and misconceptions within numeracy and algebra in compulsory school education proceed into higher education?

What features should an ILS have to support learning effectively?


Null HYPOTHESIS

There are no significant differences in learning derived from the use of an intelligent learning system and a ‘drill and practice’ computer environment


Anticipated areas of misconception

Areas Examples

W1 – Division x/6 = -18 W2 – Brackets 2(x+3)

W3 – Indices

W4 – Substituting values xy+1 if x=-4, y=6

W5 – Negative signs & values 476-z=962

W6 – Solving equations(linear) 4-2x=10-6x


Evaluating software for learning

• Pre test data and GCSE grade

• User logs• Qualitative survey criteria based

(Squires and Preece(1999))

• Group interview


Findings from trial• Users views of software for learning

• Supportive and encouraging feedback relating to the error made

• Guidance on methods of solution• Large jump between numeracy and algebra• More levels so all get some success• ‘Easy on the eye’ modern interface

• Areas of common misconception• Negative values and quantities• Brackets• Division

• Comparison of results (Treefrog, PreTest, QCA findings and survey results)

• Identification of common methods of solution


Rewriting equations• Rule based system

– recognizes if the correct finishing point is reached– checks each step of the argument for consistency

• For example, if a student enters – (x+1)^2 - x^2 = (x+1+x)(x+1-x) – both sides are expanded and gathered to 2x+1. – If one came to 1+x*2 instead, this would still

"match", as it uses the associative and commutative laws

– at each step the system checks for syntax and logical errors


Nature of dealing with expressions and equations

• A rewrite rule as a way of converting a mathematical expression in a particular domain into an equivalent one. So the rule

X + X 2*X

• A conditional rule is only applied under appropriate circumstances, such as

X^N X*X^(N-1) if N > 0• A malrule is a way of converting a mathematical

expression in a particular domain into one which may not be equivalent.

X + Y X


Intentions for the system

• Based upon Bruner’s scaffolding theory• Learn efficiently

– Minimise repetition but develop self esteem (MSC)– Level and style of support to depend on need

• Recognise the type of error and provide relevant feedback


“Drill and practice” software

• Range of question types and their applicability– 11 types – Refine to those suitable for solving numeric

expressions and solving, simplifying or factorising algebraic equations

– Boolean yes/no feedback or teacher step-by-step rigid feedback

LINK TO TREEFROG


Aims & Objectives

• describe the background which has motivated this research

• outline the intended purpose

• explain the research findings to date

• discuss future work

Using an ILS to support learning of numeracy and basic algebra

Documents

Transcript of Using an ILS to support learning of numeracy and basic algebra