Using an ILS to support learning of numeracy and basic algebra : Using an ILS to support learning of numeracy and basic algebra
Background : “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 : 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 : 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 : 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 : 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 : 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 : 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 : 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 : 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 : 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 : “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 : Aims & Objectives describe the background which has motivated this research
outline the intended purpose
explain the research findings to date
discuss future work