Samuel Otten
University of Missouri
Beth Herbel-Eisenmann
Michigan State University
Michelle Cirillo
University of Delaware
Going Over Homework in the U.S.

% of Class Time in Middle School and
High School
15-18%
GOHW
Grouws et al. (2010)
Otten, Herbel-Eisenmann, &
Cirillo (in press)
2
Discourse in GOHW

 Structure of the discourse
 Talk is typically organized around one problem at a
time
 Teacher presents answers or explanations problem-byproblem
 Students ask “questions” about the homework by
identifying a problem number
 An alternative organization is to talk across problems
by comparing/contrasting or attending to patterns in
the homework problems
Otten, Herbel-Eisenmann, & Cirillo (in press)
3
Discourse around Difficulties

 Student Errors or Difficulties in the Discourse
 Tarr et al. (2013) included the use of student
misconceptions or mistakes as a learning site within
their classroom environment protocol
 Zahner et al. (2012) found a relationship between gain
scores and incorrect responses being used as a
launching point for discussion
 These studies did not look at GOHW in particular
4
Discourse in GOHW

 Guiding Question
What was the nature of discourse around
student errors or difficulties during GOHW?
5
Method

8 math classrooms (grades 6 – 10)
Teachers varied in their background characteristics
148 Video-recorded classroom observations
Recordings were parsed by activity structure—patterned
social activities recognized by participants and shaping
their interactions (Lemke, 1990)
 Analysis focused on the instances of the GOHW activity
structure, specifically, interactions where an error or
difficulty was expressed.
 Identified categories and examined the discourse
practices within those categories




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Results

 Student errors or difficulties were relatively rare in
the GOHW discourse. Talk tended to focus on correct
explanations and correct answers to the HW items.
 When errors or difficulties did arise, they played out
in a variety of ways.
 Was the source of the error the students’ present
work or the teacher’s past experience?
 Was the error addressed indirect or direct in the
discourse?
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Errors During GOHW

Source of the Error or Difficulty
Present
The current students’ work on the assignment.
Past
The teachers’ knowledge of potential errors or
experience with past students’ errors.
Response to the Error or Difficulty
Indirect
A correct solution or approach is taken up in the
GOHW discourse that circumvents discussion of
the error or difficulty.
Direct
The error or difficulty becomes an explicit object
of focus in the GOHW discourse.
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Errors During GOHW

Most common occurrence in our data was for
the errors to arise from present students’
work and to be handled indirectly.
9
Indirect Handling of Present Errors

 Mr. M’s 8th Grade Class.
 Students have written on the board answers to homework
problems dealing with areas of compound shapes, and Mr. M is
talking through each one when he notices an error.
10
7
9
81
70
14
70
10
Indirect Handling of Present Errors

 Mr. M: “This [answer] seems off. Because … this has a
distance of 9, and this distance is gonna be 7 going up
and down there. Because the total length is 14, this
length is 7 and so that means this [other length] has to
be 7 because 7 plus 7 equals 14. That makes that 63.
Add those together, I think you get 203 for your
answer on that. If we used the same method that …
Brandon showed yesterday, you people might have
boxed it in and did an overall area of 14 times 19 and
come up with 266. This [smaller] area is 63 and you
subtract away 63 and you still get the same answer.
You have a couple of different ways of doing it.”
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Indirect Handling of Past Errors

 Teachers did raise errors from past experience or knowledge of the
content and students—for example, quickly mentioning a common
error they had seen in the past.
 Ms. H’s Advanced Algebra Class
 Evaluating an expression containing x2 with x = 3
 Ms. H: “[Three squared] is six, right? That’s a popular mistake.”
 Ms. P’s 8th Grade Class
 Assignment in which Ms. P gave students problems and solutions, but
some solutions were erroneous. Students evaluated the work and
fixed errors.
 GOHW discourse focused on students’ judgments and on the correct
solutions rather than on having students articulate the mathematical
thinking that might have underlay the errors.
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Direct Handling of Errors

 Occurred only a few times in 148 observations
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Direct Handling of Errors

 Ms. A’s Grade 7 Class
 Problem: Find a fraction and whole number whose product was
between one-half and one
 She had solicited two correct answers when she asked for
another response, calling on Sydney
 Sydney: Um, I don’t know if this is right or not, but five-ninths of
twenty-five.
 Ms. A: [writes 5/9 × 25 on the board] That’s about what fraction,
five-ninths? Close to what?
 Sydney: Half?
 Ms. A: So you want about half of twenty-five.
 Sydney: Oh.
 Ms. A: What’s wrong?
 Sydney: It’d be twelve and a half.
 Ms. A: It would be close to that, wouldn’t it? And that would not be
between half and one.
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Conclusion

 Errors arising during GOHW were predominantly
handled indirectly
 i.e., providing a correct solution rather than
investigating the reasoning or thinking behind an error
 The teachers did not ignore student thinking in
general. During other activity structures and even
when handling correct responses from students in
GOHW, they often made student thinking an explicit
object of focus in the discourse—but not with errors
or difficulties during GOHW. Why not?
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Conclusion

 Teachers may view direct handling of errors as too time
consuming or better suited for other activity structures.
 However, one could argue that handling the errors
indirectly is missing opportunities for formative
assessment as well as opportunities for student learning.
 When mathematics learning is viewed as coming to
participate in the disciplinary practices of mathematics,
direct handling of errors may provide opportunities to
explore reasoning and model perseverance through
difficulty, which are hallmarks of mathematical practice.
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Acknowledgments

 This study was supported by the National Science
Foundation (grant 0347906, Herbel-Eisenmann, PI). Any
opinions, findings, and conclusions or recommendations
expressed in this article are those of the authors and do
not necessarily reflect the views of NSF.
 We thank the teachers and students for allowing us to
work with them.
ottensa@missouri.edu
bhe@msu.edu
mcirillo@udel.edu
Twitter: @ottensam
MathEdPodcast.com
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References

 Grouws, D. A., Tarr, J. E., Sears, R., & Ross, D. J. (2010). Mathematics
teachers’ use of instructional time and relationships to textbook content
organization and class period format. Paper presented at the Hawaii
International Conference on Education, Honolulu, HI.
 Lemke, J. L. (1990). Talking science: Language, learning, and values. Norwood,
NJ: Greenwood Publishing.
 Otten, S., Herbel-Eisenmann, B. A., & Cirillo, M. (in press). Going over
homework in mathematics classrooms: An unexamined activity. Teachers
College Record.
 Tarr, J. E., Grouws, D. A., Chavez, O., & Soria, V. M. (2013). The effects of
content organization and curriculum implementation on students' mathematics
learning in second-year high school courses. Journal for Research in
Mathematics Education, 44, 683-729.
 Zahner, W., Velazquez, G., Moschkovich, J., Vahey, P., & Lara-Meloy, T. (2012).
Mathematics teaching practices with technology that support conceptual
understanding for Latino/a students. Journal of Mathematical Behavior, 31, 431446.
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