Using an ILS to support learning of numeracy and basic algebra
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Transcript of 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
Teresa FarranLecturer ICT & Mathematics Education
“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
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
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?
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
Evaluating software for learning
• Pre test data and GCSE grade
• User logs• Qualitative survey criteria based
(Squires and Preece(1999))
• Group interview
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
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
Teresa FarranLecturer ICT & Mathematics Education
“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
Teresa FarranLecturer ICT & Mathematics Education
Aims & Objectives
• describe the background which has motivated this research
• outline the intended purpose
• explain the research findings to date
• discuss future work