# Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17

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## Abstract

**:**

## 1. Introduction

## 2. The Aim of This Paper

## 3. Literature Review

## 4. Theoretical Approach

- 1
- Studies of learning and cognition, including problem-solving strategies.
- 2
- Studies of outcomes of interventions, including teaching approaches and experiments.
- 3
- Suggesting and implementing theoretical/analytic constructs or frameworks.
- 4
- Uncovering beliefs, attitudes, affects, or identities with teachers and students.
- 5
- Textbook studies, mostly of comparative nature.
- 7
- Meta studies—surveys of previous research on a given topic.

- 6
- Classroom and discourse studies;
- 8
- Analytic essays;
- 9
- Design of instruments for investigation;
- 10
- Studies of mathematics in vocations and professions.

- 1
- Conceptual or theoretical investigation.
- 2
- Qualitative empirical investigations.
- 3
- Quantitative empirical investigations.

## 5. Research Design, Method, and Methodology

#### 5.1. Methods

#### 5.2. Some Methodological Issues

## 6. Results

#### 6.1. Facts about Papers and Authors

#### 6.2. Findings of Categories of Research Study Paradigms in the Papers in NORMA17

#### 6.3. Exposing a Background for the Further Characterization of Nordic Research in DM

- Statement of problem/issue and discussion of its significance in the light of Nordic research in mathematics education or its general relevance for mathematics education research.
- Theoretical framework.
- Methodology and data analysis.

#### 6.3.1. Aspect 1: Problems or Issues Presented in the Papers and the Significance of Them According to the Authors

#### 6.3.2. Aspect 2 Theoretical Framework as Presented by the Authors

#### 6.3.3. Aspect 3 Methods and Data Analysis

#### 6.4. The Literature Review in the Papers

#### 6.5. The Role and Impact of Nordic Research in DM in Society

#### 6.5.1. Corner 1 in the Triad: Researchers

#### 6.5.2. Corner 2 in the Triad: Messages from the Researchers

#### 6.5.3. Corner 3 in the Triad: Targets or Receivers of the Messages from Researchers

#### 6.6. Short Overview of the Results in This Paper

#### 6.7. Limitations

## 7. Discussion

#### 7.1. Nordic Collaboration

#### 7.2. The Breadth of Nordic Research in Didactics of Mathematics

#### 7.3. Choice of Research Study Paradigms and Categories of Choice of Method

#### 7.4. Some Topics, Theories, and Areas of Study in Nordic Research in DM

#### 7.5. Nordic Research in DM and Society

## 8. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Early years mathematics**

**Primary mathematics**

**Secondary mathematics**

**Upper secondary mathematics**

**University mathematics**

**Communication, language and texts in mathematics education**

**Mathematics teacher education**

**Continuing professional development**

**Curricular aspects of mathematics education**

**Mathematics education in general**

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Country | Denmark | Estonia | Finland | Iceland | Norway | Sweden |
---|---|---|---|---|---|---|

3 | 0 | 6 | 1 | 16 | 6 |

Country | Denmark | Estonia | Finland | Iceland | Norway | Sweden |
---|---|---|---|---|---|---|

9 | 3 | 15 | 1 | 34 | 14 |

1 Studies of learning and cognition, including problem-solving strategies. | 10 |

2 Studies of outcomes of interventions, including teaching approaches and experiments. | 11 |

3 Suggesting and implementing theoretical/analytic constructs or frameworks. | 5 |

4 Uncovering beliefs, attitudes, affects, or identities with teachers and students. | 2 |

5 Textbook studies, mostly of comparative nature. | 3 |

7 Meta studies—surveys of previous research on a given topic. | 1 |

1 Conceptual or theoretical investigation. | 2 |

2 Qualitative empirical investigations. | 18 |

3 Quantitative empirical investigations. | 12 |

Paper | Theoretical Approach | Crucial Concepts |
---|---|---|

1 | Design research and | Trial and error, transition, odometer and |

Combinatorics | Pictographic, iconic | |

2 | Socialization theory | Qualification, socialization, subjectification |

3 | Sociocultural theory | Exploratory, cumulative, disputational |

4 | Theory of commognition | Use of words, visual mediator, narratives, routines |

5 | Number sense, place value | Quantity value, column value |

6 | Motivational theories | Expectancy value, self-efficacy |

7 | Scaffolding theory | Contingency, fading, transfer of responsibility |

8 | Sociocultural, instrumental | Epistemic, pragmatic, identity directed mediation |

9 | Content analysis | Induction basis, number of cases |

10 | Conceptual and procedural knowledge | Exploratory, evaluate |

11 | Statistical theory | Role, expl., verify, transfer, aesthetics, int.chall. |

12 | Professional language | Upbring, organize, evaluate, teach. mathematics |

13 | Statistical, measuring | Proficiency test, correlation, large sample |

14 | Statistical, measuring | Multiple choice test, Carlsten reading test, literacy |

15 | Communication, Toulmin model | Attend to, foster, argumentation, orchestrate class |

16 | Epistemological triangle | Teacher instruction, block, symbol category |

17 | Second language studies | Response category, student background category |

18 | Statistical, measuring | Attitude to learning and teaching |

19 | Knowledge quartet | Connection, transformation, contingency, foundation |

20 | MDI framework | Object of learning, exemplification, explanatory |

Paper | Data | Method | Analysis Outcome |
---|---|---|---|

1 | Written work | Picture analysis | Categorization |

2 | Questionnaire | Quantitative and qualitative | Ranking of topics valued |

3 | Video of dialogue | Interpretation of transcripts | Three types of talk |

4 | Video of talk | Finding narratives on generality Examples of gen. | |

5 | Written response | Finding mathematical focus | Examples of mathematical expr. |

6 | Questionnaire | Standard stat. description | Likert scale mean, signif. corr. |

7 | Rec. of OB actions | Text analysis of OB actions | Problem engagement and OB act. |

8 | Written answer to task | Finding CAS notation in text | Existence proof of mixed notation |

9 | Written answer to task | Finding the induction basis | Table of start. point and nb of cases |

10 | Survey | Classify five sections in video | Descript. of fours groups of answers |

11 | Questionnaire | Standard stat. description | Likert scale mean, st.dev, sign. |

12 | Validation survey | Standard stat. description | Mean value, st.dev, table of items |

13 | Written tests | Correlation coeff, scatterplot | Table of correlation coefficients |

14 | Written tests | Compare literacy and numeracy | Table of percentage of correct answers |

15 | Video of one lesson | Anal. of excerpts from lesson | Three dimensions of orchestration |

16 | Observ. of 3 classes | Identify blocks and symbols | Table of freq. of appearing blocks |

17 | Test response, survey | Analysis if text items | Tables of respon. categories/categ. |

18 | Test responses | Statistical description | Tables descriptive statistics |

19 | Observations, aud.tape | Text analysis | Example excerpts |

20 | Observation of lesson | Talk analysis | Example excerpts of explanat. talk |

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## Share and Cite

**MDPI and ACS Style**

Grevholm, B.
Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17. *Mathematics* **2021**, *9*, 803.
https://doi.org/10.3390/math9080803

**AMA Style**

Grevholm B.
Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17. *Mathematics*. 2021; 9(8):803.
https://doi.org/10.3390/math9080803

**Chicago/Turabian Style**

Grevholm, Barbro.
2021. "Recent Nordic Research in Mathematics Education Illustrated by Examples from NORMA17" *Mathematics* 9, no. 8: 803.
https://doi.org/10.3390/math9080803