An Interactive Exercise Player for Math-Bridge

**An** **Interactive** **Exercise** **Player** **for**

**Math**-**Bridge**

Johan Jeuring

Joint work with Bastiaan Heeren

Open Universiteit Nederland

School of Computer Science

S-ICT, 17 December 2009

**Math**-**Bridge**

◮ **Math**-**Bridge** is a European project, the goal of which is to

offer remedial teaching material **for** mathematics, bridging

the gap between high-schools and universities.

◮ 10+ partners, 6+ countries, 2009-2012.

◮ Multi-lingual, multi-cultural.

◮ Open standards, collaborative authoring.

◮ **Interactive** exercise player.

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

2

**Interactive** **Exercise** **Player**s

◮ **Interactive** exercise players support learning by doing.

◮ How can/should/do interactive exercise players support

learning through feedback?

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

3

Active**Math**

◮ **Interactive** math environment used in **Math**-**Bridge**

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

4

DWO **Math** Environment

◮ Applet by Freudenthal Institute **for** linear equations

The tool checks

each step

No further hints

or feedback

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

Buttons **for** the operations

Different modes **for**

solving an exercise

5

**Interactive** exercises

Ideally, interactive exercise players do more than validating

submitted answers:

◮ Present worked-out examples

◮ Provide hints how to proceed

◮ Comment on the direction of a step

A prototype applet of

DWO, extended with our

feedback services

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

6

Our approach: rewrite strategies **for** exercises

◮ Rewrite strategies specify how to solve an exercise

incrementally:

solveEquation = repeat ( Merge

Distribute

NoDivision

)

try VarLeft

try ConRight

try Scale

◮ Feedback can be calculated automatically from a strategy

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

7

Feedback services

◮ How do we realise the various kinds of feedback?

◮ A rewrite strategy is specified as a context-free grammar

over rewrite rules.

◮ A sequence of rewrite steps is a sentence of this grammar,

if it follows the strategy.

◮ Correctness of a sequence of rewrite steps can be

determined by parsing the sequence against the grammar.

◮ We offer the various kinds of feedback as services, which

are called by external exercise players.

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

8

Kind of interactions, and feedback

◮ Multiple-choice questions.

Automatically calculate not just the correct answer, but

also wrong alternatives that are based on common

misconceptions.

◮ Submitting final answers.

Canonical **for**ms. Solve a simpler exercise.

◮ Solving exercises stepwise.

Ready? Similar? Equivalent? Follow the strategy? Buggy

rule? Hints.

◮ **Exercise** completion.

Fill-in-blanks.

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

9

Services **for** mathematics

◮ Intermediate values.

Clipboard.

◮ Rounding numerical values.

Approximations only in the final step.

◮ **Exercise**s in parts.

Use contexts to store earlier parts.

◮ Implicit simplification.

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

10

Conclusions

◮ To bridge the gap in mathematical competencies between

schools and higher education, the European **Math**-**Bridge**

project provides on-line mathematics learning facilities.

◮ The Open Universiteit is responsible **for** the interactive

exercise player **for** **Math**-**Bridge**.

◮ Interactions and the kinds of feedback desired by teachers

and learning environment developers take various **for**ms.

◮ Strategies can be used to automatically calculate all these

kinds of feedback.

◮ Some mathematical exercises pose challenges to our

strategies framework, but we expect to tackle them.

◮ Experiments with >1000 students in Spring 2010.

◮ Via publishers and interactive environments, we expect to

serve >10.000 students from 2011.

[ **An** **Interactive** **Exercise** **Player** **for** **Math**-**Bridge** ]

11