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Cited by 32Mathematics Education and Teaching TechniquesStatistics Education and MethodologiesScience Education and Pedagogy

The DOI matches its Crossref record; 52 of the 59 references it cites were found in a registry or an index; 2 of the 31 sources its claims cite were checked for support.

Prospective elementary teachers use of representation to reason algebraically

Open access
Richardson, Kerri, Berenson, Sarah, Staley, Katrina·2009·The Journal of Mathematical Behavior
DOI 10.1016/j.jmathb.2009.09.002
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Overview

Integrity signals

Registry

Crossref · 10.1016/j.jmathb.2009.09.002

Cites

52 of 52 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

2 of 31 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured

  • Interpretationcitation

    Concrete materials appeared to influence the preservice teachers' algebraic thinking more profoundly than the numerical tables of data.

    “These concrete materials appeared to influence the preservice teachers algebraic thinking more profoundly than the numerical tables of data (Karpov & Haywood, 1998;Simpson, Hoyles, & Noss, 2006).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Karpov & Haywood, 1998 source
    • cites Simpson, Hoyles, & Noss, 2006 source

      The Methodology section describes school students aged 13–14, not preservice teachers. The discussion of construction and representations concerns ToonTalk models, graphs and data, but does not compare the influence of concrete materials with numerical tables on algebraic thinking. Searches for preservice teachers and that comparison found no supporting passage in our copy. (LLM, conf=0.77)

      Experimental — accuracy not yet measured
  • Findingown data

    A critical event noted in the teaching experiment related to incomplete justification.

    “Another critical event noted in this teaching experiment related to incomplete justification.”
    Quote in the paperNot a substantial claim
  • Findingown data

    Using either tabular or pattern block representations, the preservice teachers were in most cases successful in generalizing a rule that could be used for a block train of any number of blocks.

    “Using either tabular representations or the pattern block representations, the preservice teachers were, in most cases, successful in generalizing a rule that could be used for a block train of any number of blocks.”
    Quote in the paperSubstantial claim
  • Findingown data

    For square block trains, the preservice teachers wrote the equivalent of 2n+2 = P.

    “In the case of the square blocks trains, they wrote in one form or another the equivalent of: 2n+2 =P.”
    Quote in the paperNot a substantial claim
  • Findingnone given

    In the second week, an alternative generalization promoted more use of the pattern block model and less dependence on the tabular representations.

    “In the second week, an alternative generalization promoted more use of the pattern block model and less dependence on the tabular representations.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim. 25
  • It may state two separate claims as one. 28

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Simpson et al. (2006) stated that model rules can be similar despite changes in or configurations in patterns as preservice teachers noticed the similarities between triangle trains and hexagon trains.

    “Simpson et al. (2006) stated that model rules can be similar despite the changes in or configurations in patterns as preservice teachers noticed the similarities between triangle trains and hexagon trains.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Simpson et al. (2006) source

      The discussion near Figure 11 concerns students comparing parabolic motion graphs, not rules for geometric patterns. Searches for triangle and hexagon trains, pattern rules, and preservice teachers found no passage in our copy addressing the attributed example; page numbers were unavailable. (LLM, conf=0.74)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Findingown data

    Sue generated an explicit rule for perimeter and connected it to the representation of the square pattern block train.

    “She generated an explicit rule for perimeter and connected it to the representation of the square pattern block train.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data

    A third critical event noted in the teaching experiment was related to using a subtractive approach first posed by Eva in the second week.

    “A third critical event noted in this teaching experiment was related to using a subtractive approach that was first posed by Eva in the second week and described in the first critical event.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingnone given

    By the third week, the preservice teachers learned to generalize across the tasks, recognizing similarities and differences between the three different tasks.

    “By the third week, the preservice teachers learned to generalize across the tasks, recognizing similarities and difference between the three different tasks.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    Jill and Joan moved beyond reliance on the pattern block representation when they discovered the rule n(s-2)+2=P for the perimeter of an n-gon pattern block train and explained it by covering two sides when connecting shapes, multiplying the number of blocks' exposed sides, and adding two end pieces.

    “It is apparent that Jill and Joan moved beyond a reliance on the pattern block representation when they were able to discover a rule for the perimeter of an n-gon pattern block train, n(s-2)+2=P (s=number of sides in the polygon); and explained when you connect shapes, you are covering two sides so you multiply the number of blocks' exposed sides, add two end pieces.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Joan and Jill's formula 3n -2(n -1) = perimeter gave the correct answer but was not accurate in terms of their justification and should have been written (3n -2n)+ 2 = P.

    “While the formula did give the correct answer, it was not accurate in terms of their justification and instead should have been written: (3n -2n)+ 2 = P.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    In the first week, most preservice teachers focused on numerical patterns in the tabular representation, while those who referred back to the train models were most successful in finding a valid justification for their rules.

    “While most of the preservice teachers focused on numerical patterns found in the tabular representation in the first week, those who referred back to the train models were most successful in finding a valid justification for their rules.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingnone given

    While the generalizations were valid as rules, attempts to explain the algebraic symbols were incomplete with respect to explaining the origins of the coefficient and/or the y-intercept of the rule.

    “While the generalizations were valid in terms of a rule, attempts to explain the algebraic symbols of the rules were incomplete with respect to explaining the origins of the coefficient and/or the y-intercept of the rule.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Bess focused on the last block added to the train as the source of the y-intercept of 2, and this idea was persistently present in week 2 among a number of preservice teachers.

    “Bess was not alone in her focus on the last block added to the train as the source of the y-intercept of 2. This idea was persistently present in week 2 among a number of preservice teachers.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    Jill recognized the explicit rule quickly by connecting the model and the rule to justify the rule, while Joan followed in her understanding.

    “Jill recognized the explicit rule quickly by establishing a connection between the model and the rule to justify the rule while Joan followed in her understanding.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    Nearly all of the elementary preservice teachers in the teaching experiment generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment.

    “Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment.”
    • Also stated in: § 3.1.3. Week 3 · plain
      “Nearly all of the preservice teachers generalized an explicit rule, but not all were able to provide a justification for those rules.”
    • Also stated in: § 3.1.2. Week 2 · plain
      “On the second week, nearly all of the pairs generalized an explicit rule, but several were unable to offer a justification.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    Erin and Ada knew that n represented the number of blocks but did not associate the coefficient of n with a top or bottom edge because they focused on the last block or part of the model only.

    “In this case, Erin and Ada knew that the n in their rule represented the number of blocks but they did not associate the coefficient of n with a top or a bottom edge because they focused on the last block or part of the model only.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    The preservice teachers' data revealed that deeper meanings were given to the number of blocks (the variable n or x) and that the number of blocks in a train determined the perimeter, a beginning notion of covariance.

    “The preservice teachers' data revealed that deeper meanings were given to the number of blocks, the variable n or x, and that the number of blocks in a train determined the perimeter, a beginning notion of covariance.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The preservice teacher who symbolized the generalization did it inconsistently even though it resulted in the correct answer.

    “As reported, the preservice teacher who symbolized the generalization did it inconsistently even though it resulted in the correct answer.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingnone given

    The ability to express explicit generalizations symbolically continued throughout the experiment and took less time to generate each week.

    “This ability to express these explicit generalizations symbolically continued throughout the experiment and took less time to generate each week.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    The preservice teachers began with generalizing recursive rules in the first week but quickly moved on within that first day to realize the efficiency of explicit generalizations.

    “The preservice teachers began with generalizing recursive rules in the first week of the teaching experiment but quickly moved on within that first day to realize the efficiency of explicit generalizations.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Findingnone given

    The scale from these activities was based on critical events and provided a way to map the study's preservice teachers' development of algebraic reasoning over time by task in a further analysis.

    “The scale from these activities was based on critical events and provided a way to map the study's preservice teachers' development of algebraic reasoning over time by task in a further analysis.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingown data

    The authors assessed the understanding of the class of 25 preservice teachers as they progressed, over time, within each task.

    “In addition we assessed the understanding of the class of 25 preservice teachers as they progressed, over time, within each task.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    A few preservice teachers provided justifications in the first week, more in the second week, and all but two by the third week.

    “A few provided justifications in the first week, more in the second week, and all but two by the third week.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data

    The first critical event (level 1) was generalizing an explicit rule, and this event occurred each time the preservice teachers were confronted with a new pattern-finding task.

    “The first critical event (level 1) was generalizing an explicit rule and this event occurred each time the preservice teachers were confronted with a new pattern-finding task.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingnone given

    In the first week, most preservice teachers focused on numerical data in tables and had difficulty providing a valid justification for their generalizations.

    “In the first week, most focused on numerical data in tables and had difficulty providing a valid justification for their generalizations.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingnone given

    The tasks presented attainable activities for all of the preservice teachers, and while some had faster and deeper insights, they willingly shared those insights with others who were motivated to bring deeper understanding to the tasks.

    “The tasks presented attainable activities for all of the preservice teachers, and while some had faster and deeper insights, they willingly shared those insights with others who were motivated to bring deeper understanding to the tasks.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Findingnone given

    None of the other preservice teachers who justified this subtractive approach challenged this notation.

    “None of the other preservice teachers who justified this subtractive approach challenged this notation.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingown data

    Her symbolic representation of the rule did not match her verbal description but she justified the rule.

    “Her symbolic representation of the rule did not match her verbal description but she justified the rule.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationown data

    The use of isomorphic tasks promoted the preservice teachers' ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks.

    “The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and yintercept to the models constructed with pattern blocks.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Generalization and justification are overarching themes of many studies involving algebraic reasoning.

    “Generalization and justification are overarching themes of many studies involving algebraic reasoning (For example, Lannin et al., 2006;Lannin, 2005;Martino & Maher, 1999;Steele & Johanning, 2004;Zazkis & Liljedahl, 2002).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Lannin et al., 2006 source
    • cites Lannin, 2005 source
    • cites Martino & Maher, 1999 source

  • It may state two separate claims as one.

    Interpretationcitation

    The subtractive approach relied on the pattern block model and helped the preservice teachers focus on the blocks as an additional mediator of problem solving, and perhaps paved the way for justifications.

    “However, this subtractive approach relied on the pattern block model and helped the preservice teachers to focus on the blocks as an additional mediator of problem solving (Lannin, 2005), and perhaps, paved the way for justifications.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Lannin, 2005 source

  • It may state two separate claims as one.

    Interpretationown data

    Encouraging preservice teachers to apply their meanings for their symbolic representations helped them overcome initial mistaken strategies and increased their understanding of fundamental algebraic concepts.

    “By encouraging preservice teachers to apply their meanings for their symbolic representations, they overcame their initial mistaken strategies and increased their understanding of fundamental algebraic concepts.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.

    Interpretationnone given

    The justification is expected to give meaning to the symbolic rules the preservice teachers develop under the generalization.

    “More specifically, we expect the justification to give meaning to the symbolic rules the preservice teachers develop under the generalization.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Focusing on the whole pattern block train model would allow preservice teachers to focus on the entire model's complexity.

    “While focusing on individual parts is one way for preservice teachers to attempt to justify and generalize, focusing on the whole (in this case the pattern block train model) would allow preservice teachers to focus on the entire model's complexity (Armstrong & Larson, 1995).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Armstrong & Larson, 1995 source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Greer and Harel (1998) speak to isomorphisms as representational acts whereby the student is able to engage in representational thinking at varying levels.

    “Greer and Harel (1998) speak to isomorphisms as representational acts whereby the student is able to engage in representational thinking at varying levels.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Greer and Harel (1998) source

  • It may state two separate claims as one.

    Interpretationreasoning

    If first pattern-finding tasks are linear, geometric, concrete, and isomorphic, they promote classroom discourse and lead to more learning and understanding of foundational ideas in algebra.

    “We suggest that if first pattern-finding tasks are linear, geometric, concrete, and isomorphic they promote classroom discourse and lead to more learning and understanding of foundational ideas in algebra.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    Steele and Johanning (2004) in their teaching experiment used geometric patterns with 8 seventh graders and noted that some students' explicit generalizations incorporated the use of algebraic notation.

    “On the other hand, Steele and Johanning (2004) in their teaching experiment used geometric patterns with 8 seventh graders and noted that some students' explicit generalizations incorporated the use of algebraic notation.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Steele and Johanning (2004) source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Chazan and Ball (1995) argue that teachers are an important part of the mathematical discourse in a classroom.

    “Chazan and Ball (1995) argue that teachers are an important part of the mathematical discourse in a classroom.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Chazan and Ball (1995)

  • Probably not a substantial claim.

    Interpretationcitation

    'Having an image' happens when preservice teachers can keep the features of the pattern block trains in their minds and no longer have to rely on a visual, concrete representation of the train.

    “This happens when the preservice teachers can keep the features of the pattern block trains in their minds and no longer have to rely on a visual, concrete representation of the train.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    While selection of tasks is important, the way in which students are engaged in the task is of equal or even greater importance.

    “While selection of tasks is important, the way in which students are engaged in the task is of equal or even greater importance (Henningsen and Stein, 1997).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Henningsen and Stein, 1997 source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    'Teaching as telling' is rightfully criticized as a method not suitable for the development of student autonomy.

    “-Teaching as telling‖ is rightfully criticized as a method not suitable for the development of student autonomy (Kamii,1989).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Kamii,1989

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    Patterning tasks in particular contain characteristics that lend themselves well to dynamic mathematical discourse in which teachers and students intervene when needed, listen hermeneutically, and ask appropriate questions to orchestrate and extend new directions in the discourse.

    “Patterning tasks in particular contain characteristics that lend themselves well to dynamic mathematical discourse in which teachers and students intervene when needed, listen hermeneutically, and ask appropriate questions to orchestrate and extend new directions in the discourse.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds. It may state two separate claims as one.

    Interpretationnone given

    Isolating early algebra into a strand of arithmetic is problematic because it promotes little mathematical discourse and ignores the importance of the five NCTM process standards.

    “As is often done in the elementary curriculum, isolating early algebra into a strand of arithmetic is problematic because it promotes little mathematical discourse and ignores the importance of the five NCTM process standards (problem solving, reasoning and proof, communication, connections, and representation).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim.

    Premisecitation

    Zazkis and Liljedahl (2002) reported that their elementary preservice teachers had difficulty expressing generalizations of visual numerical patterns using algebraic notation.

    “These results were somewhat different from those of Zazkis and Liljedahl (2002) who reported that their elementary preservice teachers had difficulty expressing generalizations of visual numerical patterns using algebraic notation.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Zazkis and Liljedahl (2002) source

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Premisenone given

    Hermeneutical listening involves helping students seek relationships among and within tasks.

    “Hermeneutical listening involves helping students seek relationships among and within tasks.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Study design and conductnone given

    This experiment involves a relatively small number of preservice teachers and the results are considered preliminary, providing a foundation for other studies.

    “This experiment involves a relatively small number of preservice teachers and the results are considered as preliminary, providing a foundation for other studies.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Pirie and Kieren (1994) identified the preparatory activity of the growth of mathematical understanding for generalizing as 'having an image'.

    “Pirie and Kieren (1994) identified this preparatory activity of the growth of mathematical understanding for generalizing as -having an image‖ (Martin, 2008).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Pirie and Kieren (1994) source
    • cites Martin, 2008 source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Rather than interpretive or evaluative listening, which tend to focus on seeking only answers, Davis calls for hermeneutical listening to occur.

    “Rather than interpretive or evaluative listening, which tend to take on a focus of seeking only answers, he calls for hermeneutical listening to occur.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Davis (1996)

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    The two ends of any n-block train each contributed an extra unit to the perimeter when compared with the interior blocks in the train.

    “For example, the two ends of any n-block train each contributed an extra unit to the perimeter when compare with the interior blocks in the train.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Lannin et al. (2006) reported that in their pattern finding teaching experiment with spreadsheets, sixth graders had difficulty moving between recursive and explicit generalizations and incorporating algebraic notation.

    “Lannin et al. (2006) reported that in their pattern finding teaching experiment with spreadsheets, sixth graders had difficulty moving between recursive and explicit generalizations and incorporating algebraic notation.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Lannin et al. (2006) source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Davis (1996) points out the need for attention to the way in which the teacher listens to students.

    “Davis (1996) points out the need for attention to the way in which the teacher listens to students.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Davis (1996)

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.

    Interpretationnone given

    The preservice teachers' activities within their engagement in the tasks identify the attributes of the tasks that seem to make a positive difference in the outcomes, especially those involving their representations.

    “The preservice teachers' activities within their engagement in the tasks identifies the attributes of the tasks that seem to make a positive difference in the outcomes, especially those involving their representations.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationcitation

    The linear nature of all the patterns, coupled with the geometric nature of the pattern, seemed to contribute to the preservice teachers' success with the task.

    “The linear nature of all the patterns, coupled with the geometric nature of the pattern seemed to contribute to the preservice teachers' success with the task (Lannin, 2005;Steele & Johanning, 2004).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Lannin, 2005 source
    • cites Steele & Johanning, 2004 source
49 of 49

  • The authors state this as an assumption.

    The task is appropriate for the students so that they have ideas about the task that they can share with others.

    “An assumption that we make here is that the task is appropriate for the students so that they have ideas about the task that they can share with others.”
1 of 1

Citations

Cites

Flagged first, then by citations

7 of the 59 references couldn’t be matched to a known paper.

Research works printed but not linked: 2

  1. Kamii, C. (with Joseph, L.). (1989). Autonomy: The goal of education for Piaget. In C. Kamii (Ed.), Young children continue to reinvent arithmetic (second grade) (pp. 45–53). New York: Teachers College.
  2. Mason, J. (2004). Making sense of learning mathematics. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada.

Cited by

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Metadata

Authors
Richardson, K., Berenson, S., & Staley, K.
Affiliations
  • University of North Carolina at Greensboro (US)
  • North Carolina Agricultural and Technical State University (US)
Corresponding author
Richardson, Kerri
Venue
The Journal of Mathematical Behavior
Publisher
Elsevier BV
Published
2009-06
Volume
28
Issue
2-3
Pages
188-199
ISSN
0732-3123 (ISSN-L)
DOI
10.1016/j.jmathb.2009.09.002
OpenAlex
W2055500706
Semantic Scholar
dd63378957b7e11cb2767f789ced344b86772c50
Cited by
32
References
59
Citations by year
2023: 4 · 2021: 3 · 2020: 1 · 2019: 1 · 2018: 1 · 2017: 4 · 2016: 1 · 2015: 1 · 2014: 6 · 2013: 3 · 2012: 5
FWCI
9.83
Type
journal article
Language
en
Open access
Licence
www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations
  • The Journal of Mathematical Behavior (publishedVersion)
  • NC Digital Online Collection of Knowledge and Scholarship (The University of North Carolina at Greensboro) (submittedVersion)
Topics
  • Social Sciences › Education › Mathematics Education and Teaching Techniques
  • Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
  • Social Sciences › Education › Science Education and Pedagogy
Keywords
pre-service primary teachers, early algebra, algebraic generalization, pattern blocks, symbolic notation, teacher preparation, algebraic representation

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