Discussant Remarks

Discussant Remarks

Jon R. Star

Michigan State University

Tues April 11, 2006 AERA 2006 San Francisco 2

My role...

• provide constructive criticism• push your work forward• I’ve chosen to assume role of journal reviewer• allows for a conversation between reviewer

and reviewee• (I know that these are ‘just’ AERA papers!)


For starters...

• papers were great!• quality was appropriate for discussant-as-

reviewer comments• 3 of 4 full and complete papers submitted on

website prior to deadline!• apologies to Moreno and colleagues - no

comments on your paper in my remarks


Amy Ellis paper

• anticipated outlet: Journal for Research in Mathematics Education

• decision: reject, but strongly encourage revision and resubmission, taking into account my comments


1. Clarify phenomena

• distinction between types of generalization is not sufficiently clear– presence of real-life context?– or nature of reasoning?

• particularly important because curriculum A looks a lot like many that we think are good!– yet it did not necessarily support kind of

generalization that you think is productive


1. Clarify phenomena

• what is quantitative reasoning? – “creating rules that had little quantitative meaning

for them”

• what features of curriculum A do or do not support quantitative reasoning?


2. Clarify importance

• why does it matter that students reason quantitatively in this study? what does it enable students to do that other forms of generalization do not?

• evidence presented is somewhat weak• in absence of good evidence, distinction is

interesting but not obviously educationally relevant


2. Clarify importance

• is the goal to have students reason quantitatively, or by reasoning quantitatively does this allow students to do other things?– The study is not clear, either theoretically or

empirically, on this issue


3. Clarify claims

• a comparison study? yes or no?• method section says no• but results do make comments about

comparison


3. Clarify claims

• “This study’s results suggest that reasoning with quantitative relationships can support more sophisticated mathematical activity, which is a claim suggested by researchers but as yet rarely backed by empirical work examining students’ generalizations.”

• does this study’s empirical results support this suggestion, since it wasn’t comparative?


3. Clarify claims

• ‘Ellis (2006) found that middle school students who were pushed to produce generalizations focused on quantitative reasoning (as opposed to number patterns and procedures) ultimately were more likely to develop understanding of linearity.’

• does your evidence support the claims made with this sentence and citation?


Overall...

• interesting, promising, and important paper• you have a clear and well-articulated

research agenda and this paper would be another important contribution


Rozy Brar paper

• anticipated outlet: Mathematical Thinking and Learning

• decision: Revise and resubmit• good (or bad) news: reviewer thinks a lot

about conceptual and procedural knowledge!• comments and suggested revisions revolve

around this issue


1. Know vs. understand?

• What is the difference (for you) between knowledge and understanding?– you use conceptual and procedural understanding,

rather than knowledge– not an esoteric point for this paper– future work to do clinical interviews to assess

conceptual and procedural knowledge - how you assess these competencies is critical to this and future studies, so you need to be clearer


1. Know vs. understand?

• What does conceptual knowledge (or understanding?) look like in this domain?

• What conceptually is missing from the students that you interviewed?

• Not enough to say that students don’t understand what they are doing

• What exactly don’t they understand?– additional clarity on this would strength paper


2. Issue to think more about

• possible to ‘proceduralize’ almost anything• what is the potential value of things such as

area models, manipulatives, algebra tiles, real-life contexts, various software packages?

• conceptual representational crutch - an alternative representation that aims to give students insight into the conceptual underpinnings (the ‘why’) of a procedure



• is a conceptual representational crutch sufficient?

• your study says NO• some teachers don’t take full advantage of

the connections to underlying concepts that the conceptual representational crutch affords



• is a conceptual representational crunch necessary?

• can a teacher provide accessible conceptual explanations for procedural actions to students without such a crutch?

• yes - we see it a lot in TIMSS videos



• what is the potential value of the conceptual representational crutch?

• we want students to understand why they do what they do - are some representations better at achieving this goal than others?

• the conceptual representational crutch often becomes just another way to do the problem


3. Situate work in context

• excellent job of connecting work to broader rational number literature

• seems related to investigation of children’s fraction schemes - Les Steffe, Amy Hackenberg, Eric Tillema


4. Policy issues of work

• problem: students fail to develop conceptual knowledge

• worse problem: students fail to see the value of conceptual knowledge

• worst problem: we are not sufficiently clear in our research to document the benefits of having conceptual knowledge


4. Policy issues of work

• what can students do (or say) when they understand that they cannot when they don’t understand? Do you have empirical evidence that this is the case in your study?


Overall...

• interesting particularly (to me) for the way you push on (my words) the proceduralization of a conceptual representational crutch


Van Dooren paper

• anticipated outlet: Learning and Instruction• decision: accept, pending revisions• very tight study - nice contribution to a

productive line of research on this topic by authors


1. Explanation for posttest?

• analogical reasoning literature (Gentner)– difficulties that learners face in determining the

similarities between a new problem and a previously solved one

• transfer literature (Gick & Holyoak)• how might meaningful, performance-based

tasks be used AND impact posttest performance on traditional tasks?


2. Time on task

• potential confound between conditions?• P spent most time on task• just reading P problem takes longer?• time differences small enough - need to

explain away this possibility


3. Clarify analysis

• what is a “contrast analysis”• more detail and clarity on the statistical tests

that you used


Overall...

• good work!• impressed generally with the work that has

come out of this Center at University of Leuven


Closing...

• view my remarks as suggestions– feel free to disagree or challenge me

• if you do pursue publication, I am happy to read additional drafts of your work, if you would find this helpful

Thanks! (Questions?)

Jon Star

Michigan State University

[email protected]

www.msu.edu/~jonstar

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Discussant Remarks