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Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos

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Abstract

This study compared conversations among groups of teachers of high school geometry that had been elicited by a representation of instruction (either a video or an animation) and facilitated with an open-ended agenda. All artifacts used represented instruction scenarios that departed from what, according to prior work, had been hypothesized as normative. We used as the dependent variable the proportion of modal statements about instructional practice made by a group, which we argue is a good quantitative indicator that the statement appeals to the group’s knowledge of the norms of practice. Animations and videos produced similar proportion of modal statements, but the types of modal statements differed—with animations being associated with more statements of probability and obligation and videos being associated with more statements of inclination. Overall, the results suggest that animations are just as useful as videos in eliciting these sorts of orientational meanings.

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Notes

  1. Lemke (1998) renames these and adds comprehensibility, humorousness, and importance. Eggins and Slade (1997) add capacity. For our purposes, we used Halliday’s four categories.

  2. It is clear that other linguistic resources could also appeal to the audience: For example, the mood of a clause may also do that, such as when a speaker chooses to ask a question (e.g., “Is that right?”) as opposed to merely state an assertion (e.g., “that’s not right”). Also, the person of a clause, or the speaker’s choice of how to denote who is making the claim, is an interpersonal resource: When someone says “we don’t do that” instead of “I don’t do that,” this indicates an effort to involve the audience in the claim. We expect that later efforts to size up the extent to which statements made by a member of a group appeal to the group would find ways to include resources from different linguistic systems. Here we have only looked at modality.

  3. Animations can be seen in LessonSketch, www.lessonsketch.org.

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Acknowledgments

The work reported here has been supported in part by National Science Foundation grants REC-0133619, ESI-0353285, and DRL-0918425 to the first author. All opinions are those of the authors and do not necessarily represent the views of the foundation. The authors acknowledge the assistance of Annick Rougee in coding the data and the comments of Wendy Aaron to an earlier version.

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Authors and Affiliations

  1. University of Michigan School of Education, 610 East University Ave. #4119, Ann Arbor, MI, 48109-1259, USA

    Patricio Herbst

  2. Kent State University College of Education, Health, and Human Services, 401-E White Hall, Kent, 44242, OH, USA

    Karl W. Kosko

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  1. Patricio Herbst
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Correspondence to Patricio Herbst.

Appendix

Appendix

Desirability/inclination

3

2

1

−1

−2

−3

High: conviction belief?

Median: attitude

Low: undertaking

(−) Low: ~undertaking

(−) Median: ~attitude

(−) High: ~conviction

Determined

Conviction

Definitelya

Certainlya

Keen to

Pleasure to

Wonderful to

Great to

Excellent to

Good to

Miraculouslya

Fortunate to

Amazinglya

Willing to

(it’s a) commitment

“I” Would

I’d

Considering

“I” Would not

Lack conviction to

Not determined to

Not convinced that/…

Horrible

Distasteful

Alarminga

Bad

Determined not to

Convinced that isn’t

Unwilling

  1. aCross-classification with other modal type

Obligation/appropriateness

3

2

1

−1

−2

−3

High: directive

Median: advice

Low: permission

(−) Low: ~permission

(−) Median: ~advice

(−) High: ~directive

Necessary to

Needed (need to)

Responsibly

Must

Required to

Have to

Has to

Appropriate to

Appropriately

Valid to

Should

Ought to

Supposed to

Acceptable to

Acceptably

May (permissive)a

Allowed to

Permitted to

can (permissive)a

May not (permissive)a

Not Allowed to

Unnecessary to

Inappropriate to

Invalid to

Shouldn’t

Will not

Ought not

Not supposed to

Not Acceptable to not needed to

Irresponsible

Mustn’t

Not Required to

Not have to

Cannot (permissive)a

  1. aPossible cross-classification with other modal type

Warrantability/probability (comprehensibility/obviousness)

3

2

1

−1

−2

−3

High: certain

Median: probable

Low: possible

(−) Low: uncertain

(−) Median: improbable

(−) High: impossible

Will/shall

Certain(ly)a

Definitelya

Sure(ly)

Absolute(ly)

Really

Literally

Simply

Inevitab(ly)

Of course

No doubt

Indeed

Undeniably

Unquestionably

Obviously\\

Of course\\

Clearly\\

Plainly\\

(I) think

Maya

Likely

Probab(ly)

“to some extent”

Mostly

Evidently\\

Apparently\\

Presumably\\

Seemingly\\

Admitably

Arguably

Might

Cana

(I) suspect

Possibl(ly)

Roughly

So to speak

Plausible

Capableb

Able to/ability tob

Mysterious\\

Vaguely\\

Kind ofb

Sort ofb

Kindab

Sortab

Not really

Evitable

Doubtful

Questionably

Might not

Not certain

Illogical\\

May nota

Unlikely

Improbable

unapparent

Hardly\\

Can nota

Incomprehensible\\

Impossib(ly)

Implausible

Incapableb

Unable/not ableb

Certainly not

  1. \\ “Comprehensibility/obviousness”
  2. aCross-classification with other modal type
  3. b“Capability–ability”

Usuality/expectability

4

3

2

1

High: always/almost always

Median: usual

Low: rare

(−) Zero: never

Always

Usually

Sometimes

Rare/rarely

Atypical

Unusual

Surprising(ly)

Alarminga

Miraculousa

Amazinglya

Seldom

Almost

Almost never

Not often

Never

Typical

Usual

Mainly

Expectable

In most cases

Mostly

Largely

Often

Almost always

  1. aCross-classification with other modal type

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Herbst, P., Kosko, K.W. Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos. J Math Teacher Educ 17, 515–537 (2014). https://doi.org/10.1007/s10857-013-9267-y

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