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The writing on this site covers elementary and middle-school mathematics education, elementary and middle-school mathematics textbooks, as well as education research and some cognitive science.

Joshua Fisher
36 posts

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  • April 22, 2017
  • 11:30 PM
  • 164 views

Intrinsic Motivation Is Caused by Achievement

by Joshua Fisher in Text Savvy

Education interventions (specifically those dealing with mathematics education) designed to increase achievement may be better uses of time than those designed to increase intrinsic motivation.... Read more »

  • April 1, 2017
  • 02:30 PM
  • 226 views

Educational Achievement and Religiosity

by Joshua Fisher in Text Savvy

Religiosity may be correlated with lower educational achievement because people have a finite amount of time and attention, and spending time learning about religion or engaging in religious activities necessarily takes time away from learning math and science.... Read more »

  • February 26, 2017
  • 06:53 PM
  • 269 views

Expert Knowledge: Birds and Worms

by Joshua Fisher in Text Savvy

As adults with expert knowledge, we see the logical and mathematical similarities between the “how many more” and “won’t get” situations, and, thus we are easily fooled into believing that applying skills and knowledge in one task is equivalent to doing so in the other.... Read more »

  • February 4, 2017
  • 04:30 PM
  • 446 views

Hidden Symmetries

by Joshua Fisher in Text Savvy

The key ideas in the article center around (a) the standard multiplication table—with a row of numbers at the top, a column of numbers down the left, and the products of those numbers in the body of the table, and (b) modulus.... Read more »

  • January 3, 2017
  • 02:56 PM
  • 489 views

Provided Examples vs. Generated Examples

by Joshua Fisher in Text Savvy

For learning declarative concepts in a domain and then identifying those concepts in novel real-world situations, provided examples proved to be better than student-generated examples for both long-term learning and for instructional efficiency. The second experiment in the study replicated these findings.... Read more »

  • September 16, 2016
  • 09:45 PM
  • 651 views

Contiguity Effective for Deductive Inference

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/09/contiguity-effective-deductive-inference/

Even if the benefits of retrieval practice were limited to improvements in recall (as prior research has demonstrated), such improvements do not stand in the way of improvements to higher-order reasoning, such as inference-making. (And shaping the path for students, such as improving informational contiguity can have a positive effect too.)... Read more »

  • August 20, 2016
  • 09:30 PM
  • 608 views

Are Teaching and Learning Coevolved?

by Joshua Fisher in Text Savvy

Post moved to http://guzintamath.com/blog/2016/08/teaching-learning-coevolved/

Strauss, Ziv, and Stein (2002) . . . point to the fact that the ability to teach arises spontaneously at an early age without any apparent instruction and that it is common to all human cultures as evidence that it is an innate ability. Essentially, they suggest that despite its complexity, teaching is a natural cognition that evolved alongside our ability to learn.... Read more »

  • July 30, 2016
  • 07:30 PM
  • 718 views

Problem Solving, Instruction: Chicken, Egg

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/07/problem-solving-instruction-chicken-egg/

When research has more fairly compared PS-I with I-PS, it has concluded that, in general, the sequence doesn't matter all that much, though there are some positive trends on conceptual and transfer assessments for PS-I.... Read more »

  • July 18, 2016
  • 08:30 PM
  • 797 views

Interleaving Study Is Not Interleaving Learning

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/07/interleaving-learning/

In the latest research, the authors found that a blocked schedule (presenting examples from one category at a time) outperformed an interleaved schedule (interspersing examples from all the categories) for category learning when the examples to be classified were more highly discriminable. This result was consistent across the two experiments in the study (p = 0.055 and p = 0.04). Importantly, however, although interleavin........ Read more »

  • May 27, 2016
  • 12:10 PM
  • 828 views

Enhance the Salience of Relevant Variables

by Joshua Fisher in Text Savvy

Post has moved: http://guzintamath.com/blog/2016/05/enhance-salience-relevant-variables/

Performing the discrete mode of presentation test strongly enhances the salience of the relevant variable, perimeter, and somewhat decreases that of area. This enhancement supports appropriate solution strategies that lead to improved performance. This effect is robust and transfers to continuous mode of presentation for at least 10 days. In line with this conclusion, a student who performed the continuou........ Read more »

  • May 1, 2016
  • 11:00 AM
  • 746 views

Being Explicit About Symmetry

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/05/explicit-symmetry/

Working to orient oneself to the symmetries available in mathematical situations seems like one appropriate remedy to what I've called "left-to-rightism," or "cinemathematics"—a syndrome that makes us teach concepts like the equals sign (unwittingly) in a left-to-right way, such that students take away (unwittingly) the misconception that the equals sign indicates that some answer is to follow, rather than that two expressio........ Read more »

  • April 10, 2016
  • 06:30 PM
  • 724 views

Spaced Practice

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/04/spaced-practice/

Spaced practice, also called distributed practice, refers to the practice—after initial learning—of leaving gaps in time between sessions devoted to reviewing previously learned material. This stands in contrast to its much less effective counterpart, massed practice, which "crams" all of the review together in time.... Read more »

  • April 9, 2016
  • 10:00 PM
  • 966 views

Interleaving

by Joshua Fisher in Text Savvy

Post has moved: http://guzintamath.com/blog/2016/04/interleaving-inductive-learning/

Many of the misconceptions we deal with in mathematics education in particular can be seen as the result of dealing with objects of 'low discriminability' (objects that are hard to tell apart). In many cases, these objects really are hard to tell apart, and in others we simply make them hard through our sequencing.... Read more »

  • March 18, 2016
  • 11:20 PM
  • 714 views

Supporting Instructional Analogies

by Joshua Fisher in Text Savvy

Hong Kong and Japanese teachers appear to be more attentive to the processing demands of relational comparisons than are U.S teachers. Their teaching reflects the use of strategies to reduce processing demands on their students. Such differences in adherence to sound cognitive principles may have a real impact on the likelihood that students benefit from analogies as instructional tools.... Read more »

  • March 5, 2016
  • 05:30 PM
  • 852 views

Retrieval Practice Effective for Young Students

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/03/retrieval-practice-effective-students/

These results are about as straightforward as they come in the social sciences. In an article published in Frontiers in Psychology, researchers report the results of three experiments which show that the benefits of retrieval practice (practice with retrieving items from memory) extends to children as much as to adults.... Read more »

Jeffrey D. Karpicke, Janell R. Blunt, & Megan A. Smith. (2016) Retrieval-Based Learning: Positive Effects of Retrieval Practice in Elementary School Children. Frontiers in Psychology, 2-28. info:/10.3389/fpsyg.2016.00350

  • February 28, 2016
  • 12:22 AM
  • 666 views

Acquisition

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/02/acquisition/

At the moment, I would argue that modern educational thought does not pay sufficient attention to that first acquisition phase of learning. This does not seem to be a deliberate shifting of attentional resources away from Phase 1; rather, it is more a matter of conceptualizing "learning" as not having a Phase 1 at all—or a Phase 1 so straightforward and inevitable that it is of little interest to either practitioners or researcher........ Read more »

  • January 27, 2016
  • 05:50 PM
  • 845 views

Holding Back: Inhibition

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/01/holding-back-inhibition/

I remember years ago being required to write math problems containing unnecessary information so that students would have to choose the information that they needed. But just making kids do something is not the same thing as teaching them something. It is, rather, a total cave to assessment obsession—we just found a way to call assessment "instruction".... Read more »

  • January 16, 2016
  • 11:30 PM
  • 849 views

Perplexity Is Not Required for Learning

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2016/01/perplexity-not-required-for-learning/

Taken at face value, the relative lack of effect of such conflicts across a broad range of studies falsifies the cognitive conflict hypothesis: The difficulty of conceptual change must reside elsewhere than in conflict, or rather the lack thereof, between misconceptions and normatively correct subject matter.... Read more »

Ramsburg, J., & Ohlsson, S. (2016) Category change in the absence of cognitive conflict. Journal of Educational Psychology, 108(1), 98-113. DOI: 10.1037/edu0000050  

  • December 30, 2015
  • 12:10 AM
  • 878 views

Do Experts Make Bad Teachers? No.

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2015/12/experts-teachers/

A pair of new studies has found that the stereotype of the aloof professor—you know, the one that is accomplished in her field but I'd like to see her come teach the kids in my school—might be, surprise surprise, a little unfair.

Researchers found that the superior content knowledge of mathematics professors (8 assistant professors and 7 full professors) relative to secondary teachers was associated with a significantly ........ Read more »

  • December 27, 2015
  • 09:30 PM
  • 847 views

Cognitive Load Theory

by Joshua Fisher in Text Savvy

Post moved: http://guzintamath.com/blog/2015/12/cognitive-load-theory/

In some sense, a preference for explicit instruction, rather than being a pillar of cognitive load theory, is simply the logical consequence of accepting the two distinctions above—that biologically secondary and domain-specific knowledges differ significantly and qualitatively from their biologically primary, domain-general counterparts such that the former require explicit teaching whereas the latter do not.
... Read more »

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