Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies
Abstract
:1. Introduction
- (1)
- What methods/strategies of professional development interventions are used to enhance primary teachers’ mathematical modelling competencies, and what are the effects?
- (2)
- What are the effects of mathematical modelling on primary students, and how can their mathematical modelling skills be improved?
- (3)
- How can the modelling skills of primary school teachers and students be assessed?
2. Literature Review
2.1. Mathematical Modelling Competency
2.2. Mathematical Modelling Activities
2.2.1. Data Modelling
2.2.2. Modelling with Cultural and Community Contexts
3. Search Strategies and Data Analysis Methodology
3.1. Search Strategies
3.2. Data Analysis
4. Results
4.1. Statistical Analysis: Participants, Methodology, Experimental Period, and Background
4.2. RQ1: What Methods/Strategies of Professional Development Interventions Are Used to Enhance Primary Teachers’ Mathematical Modelling Competencies, and What Are Their Effects?
4.3. RQ2: What Are the Effects of Mathematical Modelling on Primary Students, and Can Their Mathematical Modelling Skills Be Improved?
4.4. RQ3: How Can the Modelling Skills of Primary School Teachers and Students Be Assessed?
5. Discussion
6. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Study (Author, Year) | Participants (Country) | Study Period | Methodology | Data | Results |
---|---|---|---|---|---|
Baker & Galanti (2017) | 8 mathematics coaches from each of the 8 division schools. (United States) | A 4-day summer institute on STEM integration and one coaching meeting a month for one year | Qualitative analysis: In-depth interviews Focus groups | Participant reflections (written documents, recording); Conversations | 8 participants expressed a willingness to use MEAs as a tool for STEM integration in their future curriculum design in grades K-6. |
English (2006) | A class of 5th graders and their teachers. (Australia) | A three-year, longitudinal teaching experiment | Qualitative analysis: Case study In-depth interviews Focus groups | Videotapes and audiotapes; Responses to the problem activity; Worksheets and final reports; The class presentations; The children’s written critiques; Field notes of classroom observations | Elementary school students of all achievement levels contribute and benefit from mathematical modeling. Children will build their own mathematical ideas, hone their communication and teamwork abilities. |
English (2010) | Three classes of first-grade children (25 to 26 students each class) and their teachers. (Australia) | The first year of a three-year, longitudinal teaching experiment; Regular half-day teacher meetings | Teaching experiment involving multilevel collaboration; Case study; In-depth interviews; Focus groups | Videotapes and audiotapes; The artefacts of all student groups; Whole-class presentations and discussions | Children’s abilities to focus their attention on the qualities of items and create a broad range of models in organizing, structuring, and representing their data. Children’s development of meta-representational knowledge. |
English (2012) | Three classes of first-grade children (25 to 26 students each class) and their teachers. (Australia) | The first year of a three-year, longitudinal teaching experiment; Regular half-day professional development meetings | Teaching experiment involving multilevel collaboration; Qualitative analysis: Case study In-depth interviews Focus groups | Videotapes, audiotapes, and digital photographs; The artefacts of all student groups; Whole-class discussions and group presentations | Results included the various ways in which children represented and re-represented collected data, and the meta-representational competence they displayed in doing so. The children who dealt with informal inference were also reported. |
English & Watson (2018) | A total of 89 students from 6th grade: 45 girls and 44 boys. (Australia) | At the end of a three-year (last half-year) longitudinal study | Intervention experiments; Design-based research; Content analysis; Statistical analysis; Case study; Focus groups | Documented in the students’ workbooks; Students’ annotations on the table of data; Transcripts of all whole class discussions and presentations | Modeling with data could develop primary school students’ statistical literacy. This modeling framework comprises four components. Currently, research received limited attention in the primary grades about modeling and inferential reasoning processes. |
English & Watters (2005) | All four 3rd-grade classes and their teachers. The principal and assistant principal attended some debriefing meetings with the teachers. (Australia) | Activities were organized weekly for a semester. More than 4 to five 40-min lessons for each problem. The teachers had several workshops on introduction, the pre- and post-meetings. | Data analysis; Ethnomethodological; Case study; In-depth interviews; Focus groups | Videotapes and audiotapes; Classroom field notes; Children’s artifacts (including their written and oral reports); Children’s responses to their peers’ feedback in the oral reports. | The modeling problems encouraged young children to develop important mathematical ideas, the metacognitive and critical thinking skills. The study has also highlighted the contributions of these modeling activities to young children’s development of mathematical description, explanation, justification, and argumentation. |
Hodgson & Wilkie (2021) | 18 in-service teachers from four primary schools (Australia) | A 5-month intervention program. Four stages of intervention (2 hours each). Another 60-min co-teaching planning meeting was appointed. | Multiple case studies; Interpretive accounts-of-practice methodological approach; In-depth interviews; Intervention experiment | Questionnaires; Audio recordings; Written documents; Research journal. | This study impelled teachers to reflect on and set goals for improving their practice. Suggestions for pre- and post-lesson protocols for productive discussions are proposed, and designing school-based professional learning processes using modeling. |
Leavy & Hourigan (2018) | 24 participants from 2nd and 3rd grade, 2 teacher educators, and 25 pre-service teachers (Ireland) | A 4-day data modeling investigation including 4 60-min lessons. | Three-tiered teaching experiment; In-depth interviews | Digital dialog; Video recording; PST’s notes, observations, and transcripts of the group conversation. | This study extended previous research as it examines young children’s modelling potential. The extension of the study over a longer duration will reap interesting findings. |
Shahbari & Peled (2015) | Two sixth-grade classes, 65 students from 6th grade in a primary school (Israel) | Three lessons | Qualitative analysis: Case study In-depth interviews Focus groups | Students’ worksheets, notes, and final models; Videotapes of student groups’ discussion. | Results showed that students utilized their knowledge of fractions in constructing mathematical models. Students had some difficulties in their knowledge of fractions. |
Yasa & Karatas (2018) | 24 preservice elementary math teachers studying their second year in the university (Turkey) | In the spring semester of one academic year. The duration of the lessons was 3 lesson hours each week. | Mixed method: Single group pretest-posttest design; Intervention experiments; | A pre-mathematical modelling test; A post-mathematical modelling test | The result showed that the instruction based on mathematical modelling improved pre-service teachers’ mathematical modelling performance. |
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Database | Search Terms | Additional Limiters |
---|---|---|
ERIC | (TI(modeling) OR TI(model-eliciting) OR TI(modelling)) AND (TI(education) OR AB(education) OR SU(education)) AND (TI(primary) OR TI(elementary) OR AB(primary) OR AB(elementary) OR SU(primary) OR SU(elementary)) AND (TI(math*) OR AB(math*) OR SU(math*)) The asterisk (*) represents any group of characters, including no character. | Full Text Peer Reviewed Language: English Date Published: -20220931 Academic Journals |
WOS | (TI = (“modeling”) OR TI = (“model-eliciting”) OR TI = (“modelling”)) AND (TI = (education) OR AB = (education) OR SU = (education)) AND (TI = (primary) OR TI = (elementary) OR AB = (primary) OR AB = (elementary) OR SU = (primary) OR SU = (elementary)) AND (TI = (math*) OR AB = (math*) OR SU = (math*)) The asterisk (*) represents any group of characters, including no character. | English Article |
Scopus | (TITLE(“modeling”) OR TITLE(“model-eliciting”) OR TITLE(“modelling”)) AND (TITLE-ABS-KEY(education)) AND ((TITLE-ABS-KEY(primary)) OR (TITLE-ABS-KEY(elementary))) AND (TITLE-ABS-KEY(math*)) | English Publication stage: Final Journal article |
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Wei, Y.; Zhang, Q.; Guo, J. Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies. Educ. Sci. 2022, 12, 923. https://doi.org/10.3390/educsci12120923
Wei Y, Zhang Q, Guo J. Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies. Education Sciences. 2022; 12(12):923. https://doi.org/10.3390/educsci12120923
Chicago/Turabian StyleWei, Yicheng, Qiaoping Zhang, and Jing Guo. 2022. "Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies" Education Sciences 12, no. 12: 923. https://doi.org/10.3390/educsci12120923
APA StyleWei, Y., Zhang, Q., & Guo, J. (2022). Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies. Education Sciences, 12(12), 923. https://doi.org/10.3390/educsci12120923