Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Education Sciences

Mastery of the concept of percentage and its representations in 2 Finnish comprehensive school grades 7-9

 Seven tasks were used to assess how 1112 Finnish grades 7 – 9 students from 13 schools across Finland their mathematical thinking using various multimodal representations.  The multimodal approaches of the participating students were in four ‘languages’ – (i) natural language, (ii) pictorial language, (iii) body language as seen through the use of tactile materials; and (iv) mathematical symbolic language. The seven percent tasks were adapted from related research by Japanese colleagues.  Students’ responses to Task 2 (Canned Salmon problem) were used to illustrate how different students were able or not, to use the four representations to solve percent problems.  The study showed that of the three different grades, year 9 students performed the best, followed by year 8 students.  The analysis provided clear data the types of questions found easiest and which were most challenging for all the three grades.  Hence the data show which concept students found most challenging for all the three grades.  Analysis of the Canned Salmon question showed that students were challenged to use mathematical language to explain their mathematical thinking despite the clear guidance provided by the Finnish Core Curriculum for Basic Education.  Educators should take note of this important finding as it challenges the belief that the answer is all that matters in mathematics.  Mathematics is more than the answer to the problem.  Rather it is equally important to be able to explain the process. The relevant literature was cited.  The two hypotheses were stated clearly and addressed in the analysis. 

Section 3 could be better structured. The heading should be Methods. Under this Section would be Tasks, Participants, Data Collection, Analysis.

I would like to read the authors’ revised version of the manuscript, particularly their address on methodological issues relating to the piloting of the tasks and why interviews were not considered as part of data collection.

Methods

Tasks –This section should focus on how the tasks for the study were selected.  Currently, under Materials and Methods, the names of the Japanese professors and the Finnish professor and affiliated university were provided.  It is unusual to do so.  It is customary to acknowledge their contributions as notes at the end of the paper.  It may more appropriate to re-write this section without stating the names of the professors.

Question: Were these items piloted before the actual collection of the data involving these 7 items?  The seven tasks identified accurately the areas where percent is used in everyday experiences.  However, Finnish students may wonder why Japan’s land mass was used in two of the questions.  Two of the 7 items used the same context: land mass, Japan and Finland.  The data showed that the performance for Q3 and Q4 were similar.  Only one item of Q3 or A4 would suffice.

The analysis of the errors made by students for Q2 was detailed and useful.

Students seemed more challenged by Q2 because the mass of the Canned Salmon sold in the current year is 120% and the year before. 

 The Canned Salmon question has the above structure.  It would be interesting to find out if the structure was reversed, as per the following structure.  The year before was 150 g, the current year is 20% more than the year before.  How would students fare with this structure?

Please see PDF copy for the structure of the questions. 

Hypothetically, the variation in structure would provide the researchers more insights into the students’ difficulties with percent.  Which particular structure challenged students more?

Participants

This section discusses the selection of the students for the study.

Data Collection

Discuss how the data were collected in this section.

Data Analysis

How the data were analysed. Although 1151 students participated in the data collection, only 1112 were accepted for analysis. 

Question:

In this study, students’ written responses were used as data to represent their mathematical thinking.  In the Discussion, it is pointed out that “expression solutions linguistically posed a significant challenge.” (p. 11 line 374).  Methodologically it would provide more insightful data if the study could have conducted interviews with some of the students after they have completed the written tasks.  The interviews could have provided these students opportunities to express themselves.  It would have provided the students with opportunities to use body language in their mathematical talk.  The presence of someone who was willing to listen to their explanations may encourage students to say more and also to illustrate their thinking.  Putting thoughts into writing is a much harder task than verbalising.  Talking to someone who is willing to listen can encourage students to talk about their mathematical thinking.

Suggestion for Conclusions Section

Overall, this is a well-written and useful paper and the education community would see benefits from the findings.  It is useful because the data shows how older, and perhaps more matured students are less challenged by the same percent questions as their younger peers.  Also, older students, rather than their younger peers, tend to use mathematical symbolism in their solutions. 

This particular finding suggests that it is more appropriate to use pictorial representations when discussing percent solutions.  It is also necessary to re-visit certain percent problems when students are older.  The Canned Salmon problem shows that maturation does not mean that older students are successful with such problems.  Teaching strategies could try to link pictorial representations with Natural language, Body language and Symbolic language. 

Lines 423 – 429: Sustainable development in education highlights the need to make mathematical knowledge practical and applicable.  Percent is the most commonly used mathematical function.  It is used in sales, good sales tax, etc.  Perhaps percent items could incorporate examples from what students see around them, there would have more opportunities to talk about mathematics.  If questions involving percent are based on land mass, then it is removed from students’ lived experiences.  Perhaps questions could involve sales during Christmas or Easter, then students may see the usefulness and importance of percent.

Line 443:  Finnish students are not well trained in expression their mathematical thinking.  This sentence then begs this question:  Who trains the students?  Are the trainers themselves aware of the importance of languaging?  It may be a good idea to ascertain the teachers’ command of languaging. 

General Comments

The figures, tables and representations are clear and easy to follow. Figure 2 was particularly useful as it provided a succinct summary of the discussion in section 2.2. 

Table 3 reports the wrong solutions to the Canned Salmon task.  APA styles accept decimals to two places. 

1.2% should be reported as 1; 2.2% should be 2. 1.7% should be 2%

Q6:  There is an error in question.  The response Increased in used in choices (a) and (c).  One of the responses should be decreased. 

Page 5, line 161, the word chapter is misleading.

Question out of curiosity:  How did students respond to Item 1- The Discount Price Item?  Did they find out how much was 30% of 20 Euros or did they work out the discount price directly (70% of 20 Euros).

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Quality of English is good.  However, there are two errors in the paper. Line 161 of p. 5.  Instead of chapter it should read as next section.

Appendix Q6 (a) and (c) both states increased.  Where is the decreased response? 

Author Response

First of all, we would like to thank you for your thoughtful and constructive feedback, which has been carefully considered. We acknowledge the shortcomings you mentioned and will do our best to address them. We are also very pleased that our article has attracted wider interest, and we are happy to respond to any questions raised.

1. “Section 3 could be better structured. The heading should be Methods. Under this Section would be Tasks, Participants, Data Collection, Analysis.”

We have done as suggested and it will certainly clarify for the reader the treatment of the survey data and analysis. The new version is in lines 211-276.

 

2. “Question: Were these items piloted before the actual collection of the data involving these 7 items? The seven tasks identified accurately the areas where percent is used in everyday experiences.  However, Finnish students may wonder why Japan’s land mass was used in two of the questions.  Two of the 7 items used the same context: land mass, Japan and Finland.  The data showed that the performance for Q3 and Q4 were similar.  Only one item of Q3 or A4 would suffice.”

 

We add lines 223-232:

For our study, we used an international set of seven tasks (Appendix A) compiled by Kumakura and his research team [31], who had previously piloted the functionality of the tasks in their own study. We adapted the task set to align with the Finnish curriculum criteria. The content of the tasks identifies areas in everyday situations where percentage calculations are needed. In two tasks, Q3 and Q4, students were asked to compare the areas of Finland and Japan. In the questionnaire, items Q3 and Q4 corresponded to items a (Q3) and b (Q4) of the same task. The aim of this task was to assess students' understanding of the concept of ratio and whether they comprehended what was being compared to what. To analyze the tasks, we renumbered task 3a and 3b, so that item a became Q3 and item b became Q4

 

3. “Question:

In this study, students’ written responses were used as data to represent their mathematical thinking.  In the Discussion, it is pointed out that “expression solutions linguistically posed a significant challenge.” (p. 11 line 374).  Methodologically it would provide more insightful data if the study could have conducted interviews with some of the students after they have completed the written tasks.  The interviews could have provided these students opportunities to express themselves.  It would have provided the students with opportunities to use body language in their mathematical talk.  The presence of someone who was willing to listen to their explanations may encourage students to say more and also to illustrate their thinking.  Putting thoughts into writing is a much harder task than verbalising.  Talking to someone who is willing to listen can encourage students to talk about their mathematical thinking. “

 

We agree. However, collecting data from many schools and a large number of students required strict student anonymity for ethical reasons and regulatory compliance. As a result, it was not feasible to contact individual respondents. Additionally, the COVID-19 pandemic caused delays in processing and analyzing the material. From an interview perspective, too much time had passed between the test completion and the potential student interviews.

 

 

4. “The Canned Salmon problem shows that maturation does not mean that older students are successful with such problems. Teaching strategies could try to link pictorial representations with Natural language, Body language and Symbolic language.”  

We definitely agree. We added this comment in the Conclusion chapter (see next section 5).

 

5. “Lines 423 – 429: Sustainable development in education highlights the need to make mathematical knowledge practical and applicable. Percent is the most commonly used mathematical function.  It is used in sales, good sales tax, etc.  Perhaps percent items could incorporate examples from what students see around them, there would have more opportunities to talk about mathematics.  If questions involving percent are based on land mass, then it is removed from students’ lived experiences. “

 

“Line 443:  Finnish students are not well trained in expression their mathematical thinking.  This sentence then begs this question:  Who trains the students?  Are the trainers themselves aware of the importance of languaging?  It may be a good idea to ascertain the teachers’ command of languaging.”

 

We made addition to Conclusion chapter (lines 470-478):

In the future, teacher training could place greater emphasis on approaches to mathematical concepts, procedures, and problem-solving that encourage students to discuss the lesson topics based on their own experiences, using pictorial and body language in addition to natural and mathematical symbolic language. This would help students build a stronger understanding of mathematical structures.

 

6. “1.2% should be reported as 1; 2.2% should be 2. 1.7% should be 2%”

Done.

 

7. “Q6: There is an error in question.  The response Increased in used in choices (a) and (c).  One of the responses should be decreased.”

Done.

  

8. “Page 5, line 161, the word chapter is misleading. “

It is now: “… detail in the subchapter 2.2.”

More comments in the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. The title of the manuscript is original, interesting, relevant, brief, in the form of phrases, logical, and in accordance with the contents of the manuscript.

2. The abstract is quite good, with novelty and state of the art is very good.

3. The manuscript proposes appropriate research questions and hypotheses, supported by relevant theories.

4. The author applies the correct and transparent methodology.

5. The research design and materials have been clearly arranged.

6. The language and presentation are clear and adequate.

7. Figures and tables are in accordance with scientific norms and standards.

8. The presentation of research results is very good, detailed and in-depth.

9. Discussion of research results is quite good.

10. Authors must follow the EJMSTE author guidelines on editorial policies and ethics.

11. The manuscript has been based on existing literature through adequate and up-to-date references.

12. The manuscript offers appropriate coverage of relevant literature.

Author Response

 

Comments and Suggestions for Authors

Thank you for the comments.

 

11. Authors must follow the EJMSTE author guidelines on editorial policies and ethics.

We have followed the instructions we received from the publisher MDPI (Template "Type of the Paper.docs"). Based on this, we have removed unnecessary lines, checked the numbering of figures and tables and corrected errors.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The necessary amendments have been made.  The revised manuscript is clear in its presentation.  

The explanation why the participants were interviewed is acceptable.