1. Katie McEldoon, Kelley Durkin & Bethany Rittle-Johnson 1

2. Instructional Time  Push to spend more time on topics to increase depth of learning (Hu, 2010)  Instructional time is limited  Need to utilize this limited time with the most effective learning activities  In math classrooms, students spend a lot of time practicing skills (Hiebert et al., 2003)  How is this instructional time best used?  Scaffolding the practice with a conceptually oriented learning activity  Completing additional practice 2

3. Conceptually Oriented Activity: Self-Explanation  Prompting students to generate explanations to themselves in an attempt to make sense of new information (Chi, 2000)  Many domains: e.g. Biology, reading, computer programming, electrical engineering  Mathematics (e.g., Atkinson, Renkl, & Merrill, 2003)  Within mathematics, self-explanation has been shown to increase both learning and transfer of knowledge to novel tasks (e.g., Rittle-Johnson 2006; Atkinson, Derry, Renkl & Wortham, 2000) 3

4. Conceptually Oriented Activity: Self-Explanation  Mechanisms of Self-Explanation  Integrates new and existing knowledge (Chi et al. 1994)  Correction of current mental model (Chi et al. 1994)  Inference rules  proceduralized into usable skills (Chi et al. 1989)  Fosters generalization (Lombrozo 2006; Rittle-Johnson, 2006)  Procedural and conceptual knowledge help each other grow (Rittle-Johnson & Alibali, 1999; Rittle-Johnson, Siegler, & Alibali, 2001)  Competence in mathematics (Hiebert, 1986) 4

5. Benefit of Extra Practice - Greater skill at applying initial problem solving strategy (Chi, Glaser, Farr 1988; Ericsson, Krampe, Tesch-Romer, 1993) - Strengthen correct strategy application, weaken incorrect strategies (Seigler, 2002) - Problem solving procedure becomes more automatized - Leaving more working memory free to acquire new and more efficient strategies (Logan 1990; Schneider, Shiffrin, 1977; Anderson, 1982, 1983, 1987; Rosenbloom & Newell, 1987) 5

6. Research Questions 1. What is the learning benefit of completing self-explanation prompts? 2. What is the learning benefit of solving additional practice problems? 3. Which use of this additional instructional time is the most beneficial for student learning? 6

7. Hypotheses 1. What is the learning benefit of completing self-explanation prompts? 1. What is the learning benefit of solving additional practice problems? 1. Which use of this additional instructional time is the most beneficial for student learning? 7 Self-explanation prompts will result in greater procedural knowledge in familiar and novel problem types Additional practice problems will result in greater procedural knowledge in familiar problem types Self-explanation will be most beneficial for student learning

8. Study Design 8 ControlSelf- Explanation Additional Practice Practice Problem 1 Practice Problem 2Self-ExplainPractice Problem 2 Practice Problem 3Practice Problem 2Practice Problem 3 Practice Problem 4Self-ExplainPractice Problem 4 Practice Problem 5Practice Problem 3Practice Problem 5 Practice Problem 6Self-ExplainPractice Problem 6 Practice Problem 4Practice Problem 7 Self-ExplainPractice Problem 8 Practice Problem 5Practice Problem 9 Self-ExplainPractice Problem 10 Practice Problem 6Practice Problem 11 Self-ExplainPractice Problem 12 Additional Instructional Time

9. Learning Domain – Math Equivalence  The notion that the equal sign means that two sides of an equation are equivalent 4 + 2 + 3 = ___ + 6 (McNeil, 2008)  Many children view the equal sign operationally, as a command to carry out arithmetic operations (Baroody & Ginsburg, 1983; Carpenter, et al., 2003; McNeil & Alibali, 2005) 4 + 2 + 3 = _9_ + 6 9

10. Design  Participants: 75 students in grades 2, 3, and 4  Procedure  Pre Test (paper & pencil)  Inclusion Criterion: <80% on pretest  Intervention (one on one)  Procedural Instruction  Practice Problems  Post Test (immediate)  Retention Test (two weeks) 10  Manipulation Here!

11. Pretest, Immediate Posttest, & Retention Test (Rittle-Johnson, Matthews, Taylor & McEldoon, 2011) 1.Procedural Knowledge Section Solving Open Equations 2 + 5 + 8 = ___ + 8 Learning Items 3 + 4 + 6 = ___ + 4 Transfer Items 8 + ___ = 8 + 6 + 4 6 - 4 + 3 = ___ + 3 2.Conceptual Knowledge Section Meaning of the Equal Sign Recognizing Valid Equation Structures Assessments 11

12. Intervention: Procedural Instruction 6 + 4 + 9 = 6 + __ 12 Instructed students on Add-Subtract strategy (Perry, 1991; Rittle-Johnson, 2006) Students asked to solve Accuracy Feedback Two Instructional Problems

13. Intervention: Practice Problems What number goes in the box? 3 + 4 + 8 =  + 8 How did you get your answer? Right/Actually, 7 is the right answer. 13

14. Study Design 14 ControlSelf- Explanation Additional Practice Practice Problem 1 Practice Problem 2Self-ExplainPractice Problem 2 Practice Problem 3Practice Problem 2Practice Problem 3 Practice Problem 4Self-ExplainPractice Problem 4 Practice Problem 5Practice Problem 3Practice Problem 5 Practice Problem 6Self-ExplainPractice Problem 6 Practice Problem 4Practice Problem 7 Self-ExplainPractice Problem 8 Practice Problem 5Practice Problem 9 Self-ExplainPractice Problem 10 Practice Problem 6Practice Problem 11 Self-ExplainPractice Problem 12 Additional Instructional Time

15. Intervention: Self-Explanation Prompts 3 + 4 + 8 = 15 + 8 Jacob got 15, which is a wrong answer. 3 + 4 + 8 = 7 + 8 Hannah got 7, which is the right answer.  HOW do you think Jacob got 15?  WHY do you think 15 is a wrong answer?  HOW do you think Hannah got 7?  WHY do you think 7 is the right answer? 15 (Siegler, 2002; Rittle-Johnson 2006)

16. Posttest & Retention Test  Immediate Posttest  Paper & pencil  Approx. 25 minutes  Retention test  Average of two weeks after intervention session  Paper & pencil  Approx. 25 minutes 16

17. Instructional Time  Intervention Total Problem Solving Time  Average Problem Solving Time per Problem: 26s 17

18. Intervention Accuracy 18  No differences by condition  No gains during additional practice problems  Low strategy Invention

19. Procedural Knowledge Analysis  Procedural knowledge:  Correct action sequences or strategies for solving problems (Rittle-Johnson & Alibali, 1999; Anderson 1993)  Assessment Procedural Knowledge Section  Solve equations with operations on both sides 4 + 5 + 8 =  + 8  Students asked to show their work  Coded for strategy use 19

20. Coding Examples  Correct Codes (5)  Equalizer: Sets up the two sides as equal 4 + 5 + 8 = 9 + 8 4 + 5 + 8 = 17 9 + 8 = 17  Incorrect Codes (3)  Add to Equal - adds up all numbers before equals sign and puts that number in blank 4 + 5 + 8 = 17 + 8 4 + 5 + 8 = 17  Blank : 4 + 5 + 8 =  + 8 20

21. Results Roadmap  Procedural Knowledge Items  Learning Items  Transfer Items  Student Performance  Correct Strategy Use  Incorrect Strategy Use  Unattempted Items  Means for post and retention test scores 21

22. Procedural Learning Items  Same equation structure as the intervention items  Same learned problem solving strategies can be applied to solve 7 + 6 + 4 = 7 + ___ 3 + 6 + 5 = __ + 5 22

23. Procedural Learning- Correct 23

24. Procedural Learning- Not Correct 24 No Significant Differences

25. Procedural Learning Summary  There is a benefit of both self-explanation and additional practice  Increased correct strategy use  Decreased incorrect strategy use  No differential performance between additional self-explanation and additional practice 25

26. Procedural Transfer Items  Items that are unlike those in the intervention session  different equation format  includes subtraction  Require a modification of the learned strategy in order to correctly solve 8 + __ = 8 + 6 + 4 6 - 4 + 3 = __ + 3 26

27. Procedural Transfer- Correct 27

28. Procedural Transfer- Not Correct 28

29. Procedural Transfer Summary  Self-Explanation benefitted procedural transfer  Increased correct strategy use  Decreased incorrect strategy use  Self-Explanation leave as many items blank as the control, but they are getting more of the attempted items correct  Additional Practice increases the number of novel problems attempted, even if they may not get them correct 29

30. Assessment Results Summary  Procedural Learning  Self-explaining and additional practice conditions had better performance than control  More correct, less incorrect strategy use  Procedural Transfer  Self-Explanation group had the best performance  More correct, less incorrect strategy use  Additional practice students attempted more novel items 30

31. Benefits of Additional Instructional Time 1. What is the learning benefit of completing self-explanation prompts? 1. What is the learning benefit of solving additional practice problems? 1. Which use of this additional instructional time is the most beneficial for student learning? 31 Self-explanation prompts resulted in greater procedural learning and transfer Additional practice problems resulted in greater procedural learning Self-explanation is the most beneficial for student learning

32. Conclusions  Self-explaining during math learning increases both procedural learning and transfer  This benefit is not just due to the additional time on task (Aleven & Koedinger, 2002; Matthews & Rittle-Johnson, 2009)  Same amount of practice as Control  Same amount of time as Additional Practice  Goal of instruction is to allow students to transfer their knowledge to novel problems  Inert Knowledge Problem (Bransford, Brown, & Cocking, 2001)  Self-Explanation is a worthwhile use of instructional time 32

33. http://peabody.vanderbilt.edu/earlyalgebra.xml Laura McLean Marci DeCaro Kristin Tremblay Maryphyllis Crean Maddie Feldman The Children’s Learning Lab The first author is supported by a predoctoral training grant provided by the Institute of Education Sciences, U.S. Department of Education, through Grant R305B040110 to Vanderbilt University. The opinions expressed are those of the authors and do not represent views of the U.S. Department of Education. 33

34. Conceptual Strategy Use  Perhaps one mechanism is the early adaptation of a conceptually oriented problem solving strategy 34

35. Explanation Quality 35

36. All Procedural Items- Correct 36 No Significant Differences

37. All Procedural Items- Not Correct 37

38. All Procedural Items Summary  No differences in correct strategy use  However, self-explanation decreased the amount of incorrect strategy use  They were leaving more items unattempted instead 38

39. Conceptual Knowledge 39

40. Compared to What  Same number of problems, same amount of time  E.g. Atkinson, Renkl, Merrill, 2003; Hilbert Renkl, Kessler & Reiss, 2008; de Bruin, Rikers & Schmidt, 2007; Grosse & Renkl, 2003; Mwangi & Sweller, 1998 40 ControlSelf Explain Practice Problem 1 Self-Explain Practice Problem 2 Self-Explain Practice Problem 3 Self-Explain Practice Problem 4 Self-Explain Practice Problem 5 Self-Explain Practice Problem 6 Self-Explain