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科教處數學教育學門 論文寫作工作坊

Comments to Lin & Tsai (manuscript)

CONCEPTUALIZING FUTURE TEACHERS’ KNOWLEDGE OF STUDENTS’ ERRORS BY USING RESEARCHED-BASED CASES

Shuk-kwan S. Leung

National Sun Yat-sen University

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For the most part, the report is clearly written and catches readers’ attention. The context for the

workshops, the research issues and their relevance to the field are well presented. The authors make a clear connection between their analysis of FT’s

learning and the cases used in the workshops.

STRENGTHS 1/2

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STRENGTHS 2/2

The results are systematically presented and the discussion of them is thorough. The paper is interesting, contains original data, and adds to our understanding of how FT learns to

handle errors.

(4)

What do you think are reviewers’

concern?

Issues reviewers may raise…

(5)

Preparing a manuscript

Limit it to the size of one paper

A separable piece with one focus

Aim at a particular journal:

JRME, ESM, IJSME, MTL

Follow guidelines for style/format

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1. INTRODUCTION

[p. 1] “Although a cohort of research has been carried out on future teachers or novice teachers’

views of students’ errors and responding to errors (Son & Sinclair, 2010; Song & Pang, 2012), and on in-service teachers’ handling student errors in classroom discourse (Ding, 2008), there are

limited attention in enhancing future teachers (FTs) knowledge of student errors”.

Suggest to follow and comment on why, could it be a matter of priority.

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2. THEORETICAL BACKGROUND

2-1 The Use of Cases in Mathematics Teacher Education

[p. 2] “With the growth of the research on the use of cases in teacher education, the functions of the use of cases can be summarized as:

collaboration, reflection, learning, and knowledge” (Markovits, & Smith, 2008).

The reference is missing and it is unclear if the work referred to FT or in-service teachers.

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2. THEORETICAL BACKGROUND

2-2 The Importance of Knowledge of Students’

Errors (KSE)

[P. 4] A good point to make here is “Shulman

(1986) has addressed the importance of handling student difficulties by putting it as a component of pedagogical content knowledge”

[p. 5] The last two paragraphs need re-structuring and there are many things in this nutshell: negative and positive knowledge, process-oriented approach, errors as prompts, students’ errors as main concept of the study, use research-based cases, assist Ft to identify and repair errors.

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2. THEORETICAL BACKGROUND

2-3 The Relationship Between the Use of Cases and Knowledge of Students’ Errors

The section can be lengthened.

It is true that case is one possible ways to

enhance teachers’ knowledge of students’ error.

However, how does “case” be compared to other ways. Comment and justify why case was chosen in this study.

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2. THEORETICAL BACKGROUND

2-4 Students’ Misconceptions on Fractions

The authors included three types of errors on fractions by Figueras, Filloy, and Valdemoros

(1985); several examples by Lawton (2005); three types by Tirosh (2000); another three by Ding

(2007); and, more examples by Leinhardt and Smith’s (1985).

Q: Based on the above prior research findings on errors regarding fraction, what is the overall

framework of this study?

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3. RESEARCH METHOD

Q:

Which method is employed?

What is the operation definition of identify,

interpret, and as well repair errors?

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3. RESEARCH METHOD

3-1 Participants

What is the definition of master teachers?

Under what setting will make 8 future teachers agreed to attend six 3-hour RBC workshop with 6 master

teachers and 14 in-service teachers [p. 7]?

Why “The 18 hours workshops in 3 days were held once a month” ? What happen in between?

Month 1: Morning: 3 hours, Afternoon: 3 hours

Month 2: Morning: 3 hours, Afternoon: 3 hours

Month 3: Morning: 3 hours, Afternoon: 3 hours

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3. RESEARCH METHOD

3-2 The RBC workshops

What make a case called RBC (Research-based case)?

How is RBC different from other cases?

How cases were presented?

Are the RBC presented in written forms or as video clips with transcription?

Explain.

3-2 The RBC workshops

What make a case called RBC (Research-based case)?

How is RBC different from other cases?

How cases were presented?

Are the RBC presented in written forms or as video clips with transcription?

Explain.

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Cite the case book

[p. 7] Six RBC on fractions from a casebook (Reference, which book?)

Q: Why these 6 discussion questions?

Appendix.

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3. RESEARCH METHOD

3-2 RBC workshops Make a Table (TRY!)

Case Grade Table X

1 3 transforming fraction with iterating units 2 fractional part more than one

3 4 renaming fraction

4 5 ordering two fractions 5 5 equivalent fractions

6 5 distinction between 1/4 box (fraction as part-whole model) and 1/4 of a box

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3. RESEARCH METHOD

3-2 The RBC workshops

Small groups:

[p. 8] That “8 FTs were distributed into different groups as possible” is unclear.

How were the 8 FT distributed among these six groups?

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3. RESEARCH METHOD

3-3 Data Collection

Item: Jing gives her fourth-grade students to solve the problem:

A box has 18 pieces of chocolates. Joseph ate 4/9 box. How many chocolates did Joseph eat? Draw a figure to show your thought.

4 students’ errors patterns ? shown in the right column were collected from Jing’s class.

(1) What can be the sources of each student error?

(2) What could be the possible strategies to

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3. RESEARCH METHOD

3-3 Data Collection

Are there errors patterns ?

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3. RESEARCH METHOD

3-3 Data Collection

Q:

Regarding the above item.

Why only four answers were chosen?

Is there a pattern?

Are these 4 students taught by the same teacher?

Is the teacher one of the participants?

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3. RESEARCH METHOD

3-3 Data Collection

Why only one test item in pre-&post- test?

Will this single item be sufficient to test knowledge on errors on fractions?

The RBC training by 6 cases involves more than what is tested in this single item: transforming fraction with iterating units; fractional part more than one; renaming fraction; ordering two

fractions; equivalent fractions; and distinction between 1/4 box (fraction as part-whole model) and 1/4 of a box (fraction as operator).

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3. RESEARCH METHOD

3-3 Data Collection

[p. 9] Only pre-post test was included here.

What data were collected in addition to pre-post test?

Did the investigators collected other data?

interview(s), video-recording of RBC workshops, diaries of facilitator, 6 master teachers, 16 in- service teachers and 8 FT; questionnaires,

worksheets..etc?

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3. RESEARCH METHOD

3-4 Data Analysis

This section needs extra work

and the procedure and steps

have to be explained further.

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4. RESULTS

The two sections are apparently rich and informative.

4-1 FTs Enhancing Knowledge of Source of Students’ Errors

4-2 FTs Enhancing Knowledge of Possible Pedagogical Strategies Handling Errors

what research questions the results can answer.

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5. DISCUSSION

The discussion section is well written.

Best if the authors indicate possible

ways in which the study can build

upon prior studies such as Lawton

(2005) or Ding (2007).

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Missing…

Q: What is the conclusion to this

study? Any implication(s)?

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Significance of study

More can be written in the front part of the paper, to justify the importance of this study. Why is

“Enhancing future teachers’ knowledge of identifying and repairing students’ errors” important to future teachers? Is it important in job search or during the beginning years of teaching? How does its importance be compared to other objectives in initial teacher

preparation? What percentage of future teachers will finally become elementary school teachers?

What if the investigators replicate the study and

addressed school teachers instead of future teachers?

(27)

Overall

Theoretical framework is needed to justify the choice of research questions and the research method. The literature consulted on fractions is appropriate but could have been more

extensive. How is it linked to a choice of RBC, data collection, data analyzes, and

interpretation on findings? Discussion. There

is no connection of findings from this study to

prior studies. Conclusion and implications.

(28)

MINOR ISSUES

Tables and figures should be typed on separate pages and attached at the back.

Spelling should be checked (e.g. Unlike denominators

http://www.englishclub.com/vocabulary/cw-unlike-dislike.htm;

International Journal of Science and Mathematics Education).

Reference. Several cited references were missing from the reference list and several references listed were not cited.

Inconsistent years such as Ding (2007 or 2008?), Richardson (1999 or 1996?), Leinhardt & Smith (1985 or 1998?).

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(30)

Thank You

NSYSU

NSYSU

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