11
Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

  • Upload
    others

  • View
    14

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

Educational Technologies

Generating Parameterized ExercisesMinko DudevAlberto González Palomo

Supervised byGeorge Goguadzeg g

14.02.2007

Page 2: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

2

Background

• Active Math▫ Exercise generatorsExercise generators

Exercise File GeneratorModified Exercise

• Randomizer▫ Parameterized exercises▫ Parameterized exercises

x+y=?x: 1, 2, 3; y: 4, 6, 6

▫ Variable replacement

Page 3: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

3

Problem description

• Current randomizer▫ Pick values from a static list▫ Pick values from a static list

• Our taskOur task▫ Pick values from given intervals

Open/closed, discrete/continuous ▫ Generate complex expressions

Composition of elementary functionsAd t d f ti t d lAdapt used functions to user model

Page 4: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

4

Selection from interval

• Parameter format▫ Discreet interval [1 10] ▫ Discreet interval [1, 10] ▫ OMDOC Format

<interval discreet="yes" left_open="no“ right_open="no"><OMOBJ><OMI>1</OMI></OMOBJ> <OMOBJ><OMI>10</OMI></OMOBJ><OMOBJ><OMI>10</OMI></OMOBJ>

</interval>

Page 5: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

5

Selection from interval

• Random number generator provides [0, 1)▫ r∈ [0 1) n ∈ [a b) n=a+r(b-a)r∈ [0, 1), n ∈ [a, b), n=a+r(b a)▫ How to get the other cases?

• (0, 1]▫ Flip interval:

r0∈ [0, 1)r=1- r ⇒ r ∈ (0 1]r=1 r0 ⇒ r ∈ (0, 1]

• [0, 1] and (0, 1)▫ r∈ [0, 1), n ∈ [a, b], n=a+r(b-a+2ε)▫ r∈ [0, 1), n ∈ (a, b), n=a+ε +r(b-a- ε)

Page 6: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

6

Random Function Composition

• OMDOC format

<parameter name="constant"><OMOBJ><OMV name= "cool_function"/></OMOBJ><function_composition>

<OMV name= “x"/> <OMV name= “y"/> y

</function_composition> </parameter>

Page 7: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

7

Random Function Composition

• Compose from▫ x+y x y x y x/y xy ex ln x sin x cos x tan x ▫ x+y, x-y, x⋅y, x/y, xy, ex, ln x, sin x, cos x, tan x,

arcsin x, arccos x, arctan x, √x, y√x• Term rewriting Term rewriting

Expression Rewrite rule Result

x x→π π

π x→sin(x) sin(π)

sin(π) x→ex esin(π)

Page 8: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

8

Random Function Composition

• User adaptation ▫ Filtering of the function candidate list▫ Filtering of the function candidate list▫ Focus function guaranteed to be used

• Depth selectionDepth selection▫ Level of difficulty

very_easy: depth=1, for instance: sin(π)easy: depth=2, for instance: esin(π)

medium: depth=3diffi lt d th 4difficult: depth=4very_difficult: depth=5

Page 9: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

9

Random Function Composition

• User adaptation diagram

User Modeluser.getMastery(f)

>50focus conceptdiffi l

Exercise Modified

50difficulty

Exercise Document

GeneratorModified Exercise

Page 10: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

10

Screenshots!

Page 11: Educational Technologies · Educational Technologies Generating Parameterized Exercises Minko Dudev Alberto González Palomo Supervised by George Goguadze 14.02.2007

11

Thank you!y