Composition Effect Kao Roll - Revision history

Alida: /* Meta-data */

2009-12-10T14:51:20Z

Meta-data

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	! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?		! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
	\|-		\|-
	\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| [[https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=314\|Geometry CWCTC 2005-2006 (PACT-AREA)]]		\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| [https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=314 Geometry CWCTC 2005-2006 (PACT-AREA)]
	\|}		\|}

Alida: /* Meta-data */

2009-12-10T14:50:50Z

Meta-data

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	! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?		! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
	\|-		\|-
	\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| ~~yes~~		\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| [[https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=314\|Geometry CWCTC 2005-2006 (PACT-AREA)]]
	\|}		\|}


	=== Abstract ===		=== Abstract ===

Koedinger: Redid the change I had previously done anonymously

2008-11-13T19:16:26Z

Redid the change I had previously done anonymously

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	! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?		! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
	\|-		\|-
	\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (~~Algebra~~) \|\| 98 \|\| 98 \|\| yes		\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| yes
	\|}		\|}

Koedinger: Undo revision 8534 by 128.2.177.115 (Talk)

2008-11-13T19:15:38Z

Undo revision 8534 by 128.2.177.115 (Talk)

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	! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?		! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
	\|-		\|-
	\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (~~Geometry~~) \|\| 98 \|\| 98 \|\| yes		\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Algebra) \|\| 98 \|\| 98 \|\| yes
	\|}		\|}


	=== Abstract ===		=== Abstract ===

128.2.177.115: /* Meta-data */

2008-11-13T19:14:02Z

Meta-data

← Older revision		Revision as of 19:14, 13 November 2008
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	! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?		! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
	\|-		\|-
	\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (~~Algebra~~) \|\| 98 \|\| 98 \|\| yes		\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Geometry) \|\| 98 \|\| 98 \|\| yes
	\|}		\|}


	=== Abstract ===		=== Abstract ===

Idoroll at 22:59, 31 March 2007

2007-03-31T22:59:03Z

← Older revision		Revision as of 22:59, 31 March 2007
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	== The Composition Effect - What is the Source of Difficulty in Problems which Require Application of Several Skills? ==		== The Composition Effect - What is the Source of Difficulty in Problems which Require Application of Several Skills? ==
	Ido Roll, Yvonne Kao, Kenneth E. Koedinger		Ido Roll, Yvonne Kao, Kenneth E. Koedinger

			=== Meta-data ===

			PI's: Ido Roll, Yvonne Kao, Kenneth E. Koedinger

			Other Contributers:
			{\| border="1"
			! Study # !! Start Date !! End Date !! LearnLab Site !! # of Students !! Total Participant Hours !! DataShop?
			\|-
			\| '''1''' \|\| 9/2006 \|\| 10/2006 \|\| CWCTC (Algebra) \|\| 98 \|\| 98 \|\| yes
			\|}


	=== Abstract ===		=== Abstract ===
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	# Heffernan, N. T. & Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society,307-312. Hillsdale, NJ: Erlbaum.		# Heffernan, N. T. & Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society,307-312. Hillsdale, NJ: Erlbaum.
	# Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.		# Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.
	# Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in		# Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education, 8, 30-43.
	Education, 8, 30-43.
	# Koedinger, K. R., & Cross, K. (2000). Making informed decisions in educational technology design: Toward meta-cognitive support in a cognitive tutor for geometry. In Proceedings of the Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA.		# Koedinger, K. R., & Cross, K. (2000). Making informed decisions in educational technology design: Toward meta-cognitive support in a cognitive tutor for geometry. In Proceedings of the Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA.
	# Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.		# Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Idoroll at 22:56, 31 March 2007

2007-03-31T22:56:02Z

← Older revision		Revision as of 22:56, 31 March 2007
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	# Bransford (2000). How people learn: brain, mind, experience, and school National Academy Press.		# Bransford (2000). How people learn: brain, mind, experience, and school National Academy Press.
	# Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., Kastberg, D., & Williams, T. (2004).		# Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., Kastberg, D., & Williams, T. (2004). Highlights From the Trends in International Mathematics and Science Study: TIMSS 2003. Washington, DC: National Center for Education Statistics.
	Highlights From the Trends in International Mathematics and Science Study: TIMSS 2003. Washington, DC:		# Heffernan, N. T. & Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society,307-312. Hillsdale, NJ: Erlbaum.
	National Center for Education Statistics.
	# Heffernan, N. T. & Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol
	production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society,307-312. Hillsdale, NJ: Erlbaum.
	# Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.		# Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.
	# Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in		# Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in
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	# Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.		# Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
	# Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77, 272-284.		# Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77, 272-284.
	# Simon, H. A., & Lea, G. (1974). Problem solving and rule induction: A unified view. In L. W. Gregg (Ed.), Knowledge and cognition. Hillsdale, NJ: Erlbaum.# Wilson, L. D. & Blank, R. K. (1999). Improving mathematics education using results from NAEP and		# Simon, H. A., & Lea, G. (1974). Problem solving and rule induction: A unified view. In L. W. Gregg (Ed.), Knowledge and cognition. Hillsdale, NJ: Erlbaum.# Wilson, L. D. & Blank, R. K. (1999). Improving mathematics education using results from NAEP and TIMSS. Washington, DC: Council of Chief State School Officers, State Education Assessment Center.
	TIMSS. Washington, DC: Council of Chief State School Officers, State Education Assessment Center.


	[[Category:Empirical Study]]		[[Category:Empirical Study]]

Idoroll at 22:54, 31 March 2007

2007-03-31T22:54:42Z

← Older revision		Revision as of 22:54, 31 March 2007
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	=== Annotated bibliography ===		=== Annotated bibliography ===

	Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E.,		# Bransford (2000). How people learn: brain, mind, experience, and school National Academy Press.
	Jocelyn, L., Kastberg, D., & Williams, T. (2004).		# Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., Kastberg, D., & Williams, T. (2004).
	Highlights From the Trends in International Mathematics		Highlights From the Trends in International Mathematics and Science Study: TIMSS 2003. Washington, DC:
	and Science Study: TIMSS 2003. Washington, DC:
	National Center for Education Statistics.		National Center for Education Statistics.
	Heffernan, N. T. & Koedinger, K. R. (1997). The		# Heffernan, N. T. & Koedinger, K. R. (1997). The composition effect in symbolizing: The role of symbol
	composition effect in symbolizing: The role of symbol		production vs. text comprehension. In Proceedings of the Nineteenth Annual Conference of the Cognitive Science Society,307-312. Hillsdale, NJ: Erlbaum.
	production vs. text comprehension. In Proceedings of the		# Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.
	Nineteenth Annual Conference of the Cognitive Science		# Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark, M. (1997). Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in
	Society,307-312. Hillsdale, NJ: Erlbaum.
	Koedinger, K. R., & Anderson, J. R. (1990). Abstract
	planning and perceptual chunks: Elements of expertise in
	geometry. Cognitive Science, 14, 511-550.
	Koedinger, K. R., Anderson, J. R., Hadley, W. H., & Mark,
	M. (1997). Intelligent tutoring goes to school in the big
	city. International Journal of Artificial Intelligence in
	Education, 8, 30-43.		Education, 8, 30-43.
	Koedinger, K. R., & Cross, K. (2000). Making informed		# Koedinger, K. R., & Cross, K. (2000). Making informed decisions in educational technology design: Toward meta-cognitive support in a cognitive tutor for geometry. In Proceedings of the Annual Meeting of the American Educational Research Association (AERA), New Orleans, LA.
	decisions in educational technology design: Toward meta-		# Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
	cognitive support in a cognitive tutor for geometry. In		# Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77, 272-284.
	Proceedings of the Annual Meeting of the American		# Simon, H. A., & Lea, G. (1974). Problem solving and rule induction: A unified view. In L. W. Gregg (Ed.), Knowledge and cognition. Hillsdale, NJ: Erlbaum.# Wilson, L. D. & Blank, R. K. (1999). Improving mathematics education using results from NAEP and
	Educational Research Association (AERA), New Orleans,		TIMSS. Washington, DC: Council of Chief State School Officers, State Education Assessment Center.
	LA.
	Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., &
	Chrostowski, S. J. (2004). Findings from IEA’s Trends in
	International Mathematics and Science Study at the
	fourth and eighth grades. Chestnut Hill, MA: TIMSS &
	PIRLS International Study Center, Boston College.
	~~Wilson, L. D. & Blank, R. K. (1999). Improving~~
	~~mathematics education using results from NAEP and~~
	~~TIMSS. Washington, DC: Council of Chief State School~~
	~~Officers, State Education Assessment Center. Bransford (2000). How people learn: brain, mind, experience, and school National Academy Press.~~
	Heffernan, N.T., & Koedinger, K.R. (1997) The composition effect in symbolizing: The role of symbol production vs. text comprehension. in proceedings of Nineteenth Annual Conference of the Cognitive Science Society, 307-12. Hillsdale, NJ: Erlbaum.
	~~Koedinger, K.R., & Anderson, J.R. (1997). Intelligent Tutoring Goes to School in the Big City. International Journal of Artificial Intelligence in Education 8, 30-43~~
	Koedinger, K. R. & Cross, K. (2000). Making informed decisions in educational technology design: Toward meta-cognitive support in a cognitive tutor for geometry. Presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
	Owen, E., & Sweller, J. (1985). What do students learn while solving mathematics problems? Journal of Educational Psychology, 77, 272-284.
	Simon, H. A., & Lea, G. (1974). Problem solving and rule induction: A unified view. In L. W. Gregg (Ed.), Knowledge and cognition. Hillsdale, NJ: Erlbaum.


	[[Category:Empirical Study]]		[[Category:Empirical Study]]

Idoroll: /* 2.214, p = .030, 2-tailed, and at post-test, t(65) */

2007-03-31T22:50:35Z

2.214, p = .030, 2-tailed, and at post-test, t(65)

← Older revision		Revision as of 22:50, 31 March 2007
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	Students were only .335 times as likely to respond correctly		Students were only .335 times as likely to respond correctly
	when the problem involved a pentagon over a triangle.		when the problem involved a pentagon over a triangle.
	Effects of Skill Composition and Shape on Complex
	Problem Performance		==== Effects of Skill Composition and Shape on Complex Problem Performance ====

	We used a binary logistic regression analysis to predict		We used a binary logistic regression analysis to predict
	the probability that students would answer a Complex		the probability that students would answer a Complex
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	model differed significantly from a model with intercept		model differed significantly from a model with intercept
	only, χ2 (6, N = 264) = 12.862, Nagelkerke R2 = .065, p =		only, χ2 (6, N = 264) = 12.862, Nagelkerke R2 = .065, p =
	.045. Overall, this model had a success rate of 64.0%,		.045. Overall, this model had a success rate of 64.0%,

	1
	p < .05, *p < 0.01
	correctly classifying 85.9% of correct responses and 28.7%		correctly classifying 85.9% of correct responses and 28.7%
	of incorrect responses. At post-test, the full model also		of incorrect responses. At post-test, the full model also
	differed significantly from a model with intercept only, χ2		differed significantly from a model with intercept only, χ2
	(6, N = 264) = 25.019, Nagelkerke R2 = .129, p < .001.		(6, N = 264) = 25.019, Nagelkerke R2 = .129, p < .001. Overall, this model had a success rate of 70.5%, correctly classifying 95.7% of correct responses and 7.9% of incorrect responses. In both models, the Outer calculation was the only significant predictor of a correct response.
	Overall, this model had a success rate of 70.5%, correctly		When the problem required an Outer calculation—in the Outer and Composite conditions—students were only .439 and .258 times as likely to respond correctly at mid-test and post-test, respectively.
	classifying 95.7% of correct responses and 7.9% of
	incorrect responses. In both models, the Outer calculation		==== Predictors of Performance on Composite Problems. ====
	was the only significant predictor of a correct response.
	When the problem required an Outer calculation—in the
	Outer and Composite conditions—students were only .439
	and .258 times as likely to respond correctly at mid-test and
	post-test, respectively.
	Predictors of Performance on Composite Problems
	We used a binary logistic regression to predict the		We used a binary logistic regression to predict the
	probability that a student would answer a Composite		probability that a student would answer a Composite Complex problem correctly on the mid-test and the post-test, given his/her success on: Inner, Outer, and Subtract, the
	Complex problem correctly on the mid-test and the post-
	test, given his/her success on: Inner, Outer, and Subtract, the
	Distracters+Rotation (DR) Simple problem that is		Distracters+Rotation (DR) Simple problem that is
	mathematically-equivalent to Outer; and the shape of the		mathematically-equivalent to Outer; and the shape of the
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	coded using three dummy variables. This model differed		coded using three dummy variables. This model differed
	significantly from a model with intercept only for both mid-		significantly from a model with intercept only for both mid-
	test, χ2 (7, N = 66) = 26.567, Nagelkerke R2 = .442, p <		test, χ2 (7, N = 66) = 26.567, Nagelkerke R2 = .442, p < .001, and post-test, χ2 (7, N = 66) = 30.466, Nagelkerke R2 =
	.001, and post-test, χ2 (7, N = 66) = 30.466, Nagelkerke R2 =
	.495, p < .001. The mid-test model had overall success rate		.495, p < .001. The mid-test model had overall success rate
	of 75.8%, correctly classifying 75.0% of correct responses		of 75.8%, correctly classifying 75.0% of correct responses
	and 76.5% of incorrect responses. The post-test model had		and 76.5% of incorrect responses. The post-test model had
	an overall success rate of 77.3%, correctly classifying		an overall success rate of 77.3%, correctly classifying 83.8% of correct responses and 69.0% of incorrect
	83.8% of correct responses and 69.0% of incorrect
	responses.		responses.
	The significant predictor variables in the model changed		The significant predictor variables in the model changed
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	correctly were 6.366 times more likely to answer Composite		correctly were 6.366 times more likely to answer Composite
	correctly. Shape was not a significant predictor at either		correctly. Shape was not a significant predictor at either
	mid-test or post-test. These results are presented in Table 4.		mid-test or post-test. These results are presented in Table 1.

	Assessing the Difficulty of Spatial Parsing We took		==== Assessing the Difficulty of Spatial Parsing ====
	Accuracy(Outer) × Accuracy(Inner) × Accuracy(Subtract)
			We took Accuracy(Outer) × Accuracy(Inner) × Accuracy(Subtract)
	and compared this to Accuracy(Composite) for each student		and compared this to Accuracy(Composite) for each student
	using a paired, 2-tailed t-test. This difference was		using a paired, 2-tailed t-test. This difference was
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	significantly between the Outer and DR at either mid-test,		significantly between the Outer and DR at either mid-test,
	t(65) = -.851, p = .398, or post-test, t(65) = -1.356, p = .180.		t(65) = -.851, p = .398, or post-test, t(65) = -1.356, p = .180.
	~~Discussion~~
	~~We will return to our original hypotheses to begin the~~
	~~discussion. It was clear that distracters had a negative~~
	~~impact on Simple performance at mid-test, although this~~
	~~effect had largely disappeared by post-test. Although we~~
	~~did not find significant effects of Rotation on Simple~~
	~~performance, we did find evidence that many students~~
	~~simply rotated the paper until they were viewing the figure~~
	~~in a standard orientation, effectively negating our Rotation~~
	~~manipulation. Thus, our first hypothesis is partially~~
	~~supported.~~
	~~We did find a composition effect in area problems, and~~
	~~the probability of success on Composite problems could not~~
	~~be predicted by simply multiplying the probabilities of~~
	~~success for the three subproblems. Thus, our second~~
	~~hypothesis is supported.~~
	~~We only found partial support for our hypothesis that the~~
	~~source of the composition effect is due to the diagram~~
	~~parsing load.~~ ~~We did find that the probability of success on~~
	~~Composite problems was greater than the product of~~
	~~probabilities for the three subproblems, but only at mid-test.~~
	~~In addition, there were no significant differences between~~
	~~Outer and DR at either mid-test or post-test, although we~~
	~~feel it is worth noting that the data are trending in the~~
	~~predicted direction, with Outer being more difficult than DR~~
	~~on both mid-test and post-test. Finally, our P(Composite) =~~
	~~P(Simple Outer Eq.) × P(Inner) × P(Subtract) model did a~~
	~~good job of predicting actual performance on Composite~~
	~~problems.~~
	~~To conclude our discussion, we would like to address the~~
	~~differences between performance at mid-test and~~
	~~performance at post-test and the implications for designing~~
	~~instructional interventions. First, we would like to note that~~
	~~instruction in the Area Composition unit of the Geometry~~
	~~Cognitive Tutor was able to improve performance on all~~
	~~skills, not just skills new to composite problems. This~~
	~~suggests that students may not have fully mastered the~~
	~~single-step area skills prior to beginning Area Composition,~~
	~~but that Area Composition continues to provide practice on~~
	~~these skills. Furthermore, the single-step skill practice in~~
	~~the Area Composition unit seems particularly effective at~~
	~~removing the effects of distracters on performance. This~~
	~~makes a great deal of intuitive sense if you consider~~
	~~composite area problems to inherently contain distracters.~~
	~~Second, although we did not find strong support for our~~
	~~contention that spatial parsing is difficult for students, we~~
	~~feel that training students to quickly identify important~~
	~~perceptual chunks can still have a positive impact on~~
	~~performance. If, for example, students were trained to look~~

	=== Explanation ===		=== Explanation ===

Idoroll at 21:31, 31 March 2007

2007-03-31T21:31:52Z

@@ Line 163: / Line 163: @@
 An alpha value of .05 was used for all statistical tests.
 ==== Comparison of Mid-test and Post-test Performance ====
 Scores on the pretest were at floor, ranging from 0 to 50%
@@ Line 179: / Line 180: @@
 = 2.214, p = .030, 2-tailed, and at post-test, t(65) = 2.355, p
 = .022, two-tailed.  These results are presented in Table 1.
 ==== Effects of Distracters, Orientation, and Shape on
-Simple Problem Performance ====
+==== Effects of Distracters, Orientation, and Shape on Simple Problem Performance ====
 We used a binary logistic regression analysis to predict the
-probability that students would answer a Simple problem
+We used a binary logistic regression analysis to predict the probability that students would answer a Simple problem correctly on the mid-test and the post-test.  Distracters, Rotation, and three dummy variables coding diagram shape—parallelogram, pentagon, trapezoid, or triangle - were entered into the equation as predictors.
-Table 1: Mean performance on mid-test and post-test by
+Table 1: Mean performance on mid-test and post-test by diagram type1
 At mid-test, the full model differed significantly from a
 model with intercept only, χ2 (5, N = 264) = 17.884,