Serendip is an independent site partnering with faculty at multiple colleges and universities around the world. Happy exploring!

Faculty Learning Community: Agenda and Notes (February 18, 2010)

Anne Dalke's picture

SUGGESTED READING below, provided by Julie Booth of Temple University, who will facilitate the conversation.
Snacks will be served in CAMPUS CENTER 200.
Please invite other interested people to join these conversations. Those of you who hope to join
via conference call should contact Howard Glasser before Thursday to work out arrangements.

From Julie Booth:
Hello all!
Thank you for inviting me to participate in your group. I look forward to meeting you!

Just a bit of background on me: I’m an assistant professor in the department of Psychological Studies in Education at Temple University. I completed my PhD in Developmental Psychology at Carnegie Mellon University and trained as a postdoctoral fellow with the Pittsburgh Science of Learning Center. My work focuses broadly on the development of mathematics skills and how prior knowledge affects learning in math. I have studied numerical magnitude representation in elementary school and currently focus on the development of pre-algebraic and algebraic skills. In all cases, I aim to develop instructional interventions to fill gaps in students’ knowledge and improve learning.

At Thursday’s meeting, I will present findings from a recent study in which we adapted typical algebra assignments to be more in line with a large body of work from the field of cognitive science that suggests that a combination of explaining worked examples and solving problems is a more effective use of student time than problem-solving practice alone. In our assignments, we directly target critical student misconceptions in order to improve both their conceptual and procedural knowledge of algebraic equation-solving. The attached file describes the theoretical motivation for our work.

Discussion will center around the following questions:
1 .Why does this approach enhance student learning? Are there certain populations of students who may benefit more than others, and why?

2. Would this approach be useful in all math/science domains, and how would it need to be adapted to best target key learning goals in other domains?

3.With such a strong literature supporting this approach, why does it rarely occur in typical classrooms—both K-12 and college? This problem is not just limited to the worked example approach. Why do research findings often fail to make their way into classroom practice? How can we be more effective at dissemination to make sure that real-world students benefit from the work that we do?

Bryn Mawr College


18 pt
18 pt


/* Style Definitions */
{mso-style-name:"Table Normal";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
font-family:"Times New Roman";
mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";

Theoretical Motivation for the Transforming Algebra Assignments project
Laboratory research findings from the field of Cognitive Science suggest several methods of improving students’ conceptual and procedural knowledge, including interleaving worked examples into problem-solving activities and prompting students to self-explain responses.  Both techniques are recommended by the IES Cognition Practice Guide as useful methods for instruction (Pashler et al., 2007).
In worked examples, students are asked to study solutions rather than solve problems themselves. Positive effects of interleaving worked examples (i.e., alternating between problems and examples within problem-solving activities) have been reported in a variety of courses teaching well-defined problems (Clark & Mayer, 2003), including Algebra (Sweller & Cooper, 1985). Worked examples of problem solutions are more efficient for learning new tasks because they reduce the load in working memory (compared with completing long strings of practice problems), thereby allowing students to learn the steps in problem solving (Sweller, 1999).
Self-explanation is explaining information to oneself as one reads or attempts to learn.  Numerous empirical results have supported the notion that self-explanation improves learning (see Chi, 2000, for a review); the benefits of self-explanation include integrating various pieces of knowledge (either from the instructional material, their own prior knowledge, or between the two), generating inferences to fill gaps in one’s own knowledge, and making the new knowledge and the connections that they’ve generated explicit (Roy & Chi, 2005; Chi, 2000).  
Implementation of these techniques for learning traditionally involves presenting students with a correct problem solution and asking them to explain why it is correct. However, students may also benefit by explaining incorrect problem solutions. Ohlsson’s (1996) theory of learning suggests that beginning learners benefit from the act of detecting an error, identifying the faulty knowledge or misconception that caused the error, and explaining how their knowledge must be changed in order to make it correct.  In addition, overlapping waves theory (Siegler, 1996) posits that individuals know and use a variety of strategies for any type of problem, and that good strategies gradually replace ineffective ones; for more efficient change to occur, learners must reject their ineffective strategies, which can only happen if they understand both that the procedure is wrong and why it is wrong (i.e., which problem features make the strategy inappropriate) (Siegler, 2002).  Consistent with these ideas, asking students to explain why incorrect answers are incorrect is a common method of instruction in Japan, where mathematics achievement is consistently outstanding by world standards (Stevenson & Stigler, 1992). Further, a growing number of empirical laboratory studies confirm that asking students to explain incorrect, as well as correct, solutions leads to greater learning than only asking them to explain correct answers (Siegler & Chen, 2008; Rittle-Johnson, 2006).
We believe that in the case of algebraic equation solving, each type of example—correct and incorrect—has distinct and important benefits, which complement each other to produce better conceptual and procedural learning. Studying correct examples increases or strengthens students’ knowledge of procedures, and answering the self-explanation questions draws their attention to important features in the examples and helps them to construct an understanding of the role of those features in the problem. Studying incorrect examples weakens incorrect procedural knowledge, as it helps students to accept that the procedures are wrong; answering the probing questions draws students’ attention to the differences in features between the presented problem and others where a procedure does work, which likely remedies misconceptions, and prompts conceptual improvement. 
Despite the abundant evidence asserting the benefit of these practices, a chasm exists between research on learning and common practices in the classroom (National Research Council, 2002).  A widespread and important instance of this chasm is the ubiquitous approach to problem-solving practice in STEM courses, in which students are typically given sets of problems to solve on their own. In a survey of eleven Algebra assignments collected from Minority Student Achievement Network (MSAN) school districts, almost all of the items (~95%) in each assignment were problems to solve. Of the 128 items across all of the assignments, only six requested an explanation and only one provided a worked example of a problem solution. A quick scan of nearly any traditional STEM textbook will reveal the same: Practice activities consist of problems to solve with few examples to study and few prompts to explain.
That empirically-proven instructional techniques do not seem to find their way to the classroom is a common problem; teachers are often resistant to making large-scale changes to their curriculum and classroom routines because it destabilizes instruction and introduces uncertainty (Kennedy, 2005). In the present study, we test the effectiveness of incorporating self explanation of worked examples into assignments that students complete independently. In this way, students can get the benefit of the exercises without requiring major changes in instruction.

Meeting Summary and Continued Conversation below



Post new comment

The content of this field is kept private and will not be shown publicly.
To prevent automated spam submissions leave this field empty.
4 + 2 =
Solve this simple math problem and enter the result. E.g. for 1+3, enter 4.