Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

Figures & data

Figure 1. Two examples of paired problems: item 6 and item 12.

Table 1. Task characteristics of 21 paired problems.

Domain	Task	Item	Wordiness	Pictorial Complexity
Numbers	TV + dvd	4	26	2
	Change	5	19	2
	Money pile	9	36	2
	Kitchen tiles	12	35	2
	Hamburgers	16	21	2
	Coughing syrup	17	36	3
	Public debt	18	18	2
Proportions	Travel time	3	29	2
	Recipe	6	44	1
	Price magazine	7	36	2
	AEX index	8	30	3
	Scale model	10	23	2
	Endive	15	9	1
	Winter tires	20	40	3
Measurement & Geometry	Apples in bag	1	23	2
	Gas usage	2	30	2
	Double glazing	11	27	2
	Water bottles	13	19	2
	Bedroom tiles	14	38	3
	Cake tin	19	17	1
	Chocolate boxes	21	51	4

Note: Wordiness is number of words used in the description of the problem situation (A-version, Dutch version). Pictorial Complexity is the number of visual elements in the depictive representation (B-version, Dutch version).

Table 2. Number of participants in school types and age groups.

School Type	Age	n
Primary (grade 5 and 6)	11–12	969
Secondary	12–18	29,067
Vocational	16–20	1,556

Note: n is number of participants

Table 3. The difference in students’ performance on task level.

Item	N		M (SE)		t test
	version A	version B	version A	version B	P (|T|>|t|)
1	15,878	15,964	.716 (.004)	.720 (.004)	.424
2	15,986	15,856	.525 (.004)	.483 (.004)	.000***
3	15,785	16,057	.314 (.004)	.290 (.004)	.000***
4	15,835	16,007	.826 (.003)	.833 (.003)	.131
5	16,038	15,804	.720 (.004)	.828 (.003)	.000***
6	15,775	16,067	.631 (.004)	.640 (.004)	.102
7	16,065	15,777	.404 (.004)	.416 (.004)	.042
8	16,298	15,544	.303 (.004)	.299 (.004)	.420
9	16,069	15,773	.221 (.003)	.213 (.003)	.085
10	15,882	15,960	.495 (.004)	.525 (.004)	.000***
11	15,850	15,992	.145 (.003)	.310 (.004)	.000***
12	15,871	15,971	.466 (.004)	.438 (.004)	.000***
13	15,931	15,911	.619 (.004)	.641 (.004)	.000***
14	15,889	15,953	.040 (.002)	.046 (.002)	.080
15	15,793	16,049	.394 (.004)	.388 (.004)	.264
16	15,921	15,921	.803 (.003)	.815 (.003)	.005
17	15,986	15,856	.803 (.003)	.787 (.003)	.000***
18	15,847	15,995	.153 (.003)	.168 (.003)	.000***
19	15,932	15,910	.247 (.003)	.284 (.004)	.000***
20	15,925	15,917	.130 (.003)	.164 (.003)	.000***
21	16,044	15,798	.188 (.003)	.256 (.003)	.000***

Note: N is number of items tested. M is mean score on items (with standard error in parentheses) P(|T|>|t|) is result of t test, unpaired, unequal with hypothesis that difference in score is 0; ***p < .001. Version A is the word problem; Version B is the image rich numeracy problem; Significant results are underlined.

Table 4. Probit model expanded with task characteristics: wordiness and number of depictive elements.

Variable		Model expanded with task characteristics regarding wordiness and number of depictive elements.
		Coefficient(SE)	Marginal effect(SE)
Version (A = 0, B = 1)	α1	.059*** (.010)	.023*** (.004)
Primary education	α2,1	−.547*** (.017)	−.200*** (.005)
Secondary general	α2,2 - α2,6	−.059*** (013)	−.024*** (.005)
Vocational education	α2,7	.328*** (.016)	.130*** (.006)
Grade	α2,8	.232*** (.002)	.092*** (.001)
Gender	α2,9	.114*** (.003)	.045*** (.001)
Ethnicity	α2,10	−.150*** (004)	−.059*** (.002)
Relative age	α2,11	−118*** (002)	−.047*** (.001)
Last math grade	α2,12	.052*** (001)	.021*** (000)
# Words (Version A)	α2,13	−.016*** (.000)	−.006*** (000)
# Depictive elements (Version B)	α2,14	−.221*** (.003)	−.087*** (.001)
Constant	α0*	−.547*** (.017)

Note: α_i,j is the coefficient in the probit model, α₀*= -δ + α₀. Coefficients are calculated with maximum likelihood by STATA11, standard errors are in parentheses. The measure of good fit pseudo-R² = .040 (McFadden’s R²). All variables are significant ***p < .001. The effect of Number of words is only analysed for the word problems (version A); The effect of Number of depictive elements is only analysed for the image-rich numeracy problems (version B).

Table 5. Probit model expanded with variables regarding content domain.

Variable		Model expanded with item characteristics regarding content domain
		Coefficient(SE)	Marginal effect(SE)
Version (A = 0, B = 1)	α1	.037*** (.006)	.014*** (.002)
Primary education	α2,1	−.561*** (.017)	−.205*** (.005)
Secondary general	α2,2 - α2,6	−.060*** (.013)	−.024*** (.005)
Vocational education	α2,7	.335*** (.016)	.133*** (.006)
Grade	α2,8	.236*** (.002)	.093*** (.001)
Gender	α2,9	.117*** (.003)	.046*** (001)
Ethnicity	α2,10	−.153*** (004)	−.060*** (002)
Relative age	α2,11	−.120*** (002)	−.047*** (.001)
Last math grade	α2,12	.053*** (001)	.021*** (.000)
Numbers	α2,15	reference	reference
Proportions	α2,16	−.494*** (.006)	−.191*** (.002)
Meas. & Geom.	α2,17	−.567*** (.006)	−.218*** (.002)
Numbers × Version	cross term	reference	reference
Proportions × Version	cross term	−.016 (.008)	−.006 (.003)
Meas.& Geom.× Version	cross term	.060*** (.008)	.024*** (.003)
Constant	α0*	−.675*** (.016)

Note: α_i,j is the coefficient in the probit model, α₀*= -δ + α₀. Coefficients are calculated with maximum likelihood by STATA11, standard errors are in parentheses. The measure of good fit pseudo-R² = .056 (McFadden’s R²). All variables are significant ***p < .001, with the exception of proportions × version.

Figure 2. Paired problem 11: Double-glazing.