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### Session chair: Jónína Vala Kristinsdóttir

## Paper 1: Achievement emotions, self-concept, and value in Norwegian school beginners’ mathematics studies

**Anna Maria Rawlings, Department of Special Needs Education, University of Oslo and Faculty of Educational Sciences, University of Helsinki, anna.rawlings@helsinki.fi. ****Co-authors: Markku Niemivirta, Johan Korhonen, Marcus Lindskog, Heta Tuominen,and Riikka Mononen**

### Abstract

Mathematics-related enjoyment, anxiety, and boredom are seen as reciprocally related with mathematics achievement, in a potentially long-lasting, beneficial or detrimental cycle, as regards both academic careers and overall well-being (e.g., Camacho-Morles et al., 2021; Namkung et al., 2019). However, there is a paucity of longitudinal studies investigating the prevalence and development of these emotions, their relationships with performance, and possible phenomena contributing to them, during the early school years (Namkung et al., 2019). In the present study, therefore, we chart the levels, interrelationships, and development of mathematics-related enjoyment, anxiety, and boredom, over the course of the first three school years. Following suggestions from the control-value theory (Pekrun, 2006), we consider mathematics self-concept, mathematics value, and arithmetic skills as factors potentially contributing to students’ emotions, as well as the influence of these factors on later mathematics performance.

Participants are Norwegian school-beginners (*N *= 262; *Mage *= 6 years 9 months, *SDage *= 3.43 months at beginning of data collection; girls 45.4 %) from 12 classes in five schools in the metropolitan area of Oslo, Norway. The children were tested as part of a larger data collection in a project focusing on children’s early numeracy development. Data collection began in the spring term of the first grade (t1) and continued in the autumn term of the second grade (t2). Planned data collection for the spring term of the second grade was cancelled due to the covid-19 pandemic; however, further data were collected in the autumn term (t3) and the spring term (t4) of the third grade.

The participating children rated their enjoyment (6 items, e.g., “*I enjoy doing math*”), anxiety (7 items, e.g., “*Math scares me*”), and boredom (7 items, e.g., “*I find doing math boring*”) on a 5-point Likert-type scale (AEQ-ES; Lichtenfeld et al., 2012), with the anchor values depicted by pictures of children’s faces showing increasing emotional intensity. Mathematics self-concept (e.g., “*Doing mathematics is easy for me*”) and mathematics value (“*I think mathematics is interesting/important/useful*”) were measured with three items each, likewise on a 5-point scale (CIVM; Niemivirta et al., 2018), with emoticon faces indicating 1 = *not at all *to 5 = *very much*. Arithmetic performance was measured as addition and subtraction fact fluency using a standardized test (Klausen & Reikerås, 2016) at t1 and t3, and with curriculum-based mathematics tests at t2 and t4. Analyses are conducted using Mplus statistical software, with factor structure and measurement invariance tested by running a series of confirmatory factor analyses (CFA), and the longitudinal relationships with latent growth curve modeling (LGCM).

Initial CFAs confirmed the expected model of three factors, corresponding to enjoyment, anxiety, and boredom (χ2 (1674) = 2020.411, *p *< .001; RMSEA = .029 (90% CI .024, .033); CFI = .980; WRMR = 1.005), and measurement invariance of this three-factor model over time was established. We will continue further with LGCM and examine potential antecedents of the initial levels and changes in achievement emotions, by adding as predictors the students’ mathematics self-concept, mathematics value, arithmetic skill level, and gender. Finally, statistical power permitting, we will conduct a full growth model by adding students’ mathematics performance at the end of the third grade (t4) as an outcome. Full results will be presented and discussed at the NORSMA conference.

## Paper 2: Low performers only recognize straightforward addition word problems

**Pernille Pind, Forlaget Pind og Bjerre, pindogbjerre@gmail.com. Co-authors: Peter Sunde & Pernille B. Sunde **

#### PRESENTATION (PDF)

### Abstract

Word problems provide context to mathematics, and can be seen as a connection between mathematics and the real world. Word problems are also considered to be among the most difficult problems students encounter^{1}. When students first experience word problems, the problems are often so easy to comprehend that the students solve them ‘in the head’ without the need of recognizing the matching symbolic problem. To solve more complex word problems, it is necessary to be able to recognize the arithmetic situation. Otherwise, the student will not be able to use a calculator, which is often an important issue for low performers. Word problems can be categorized in different semantic types. E.g. for one-step addition problems three different additive situations can be recognized: *combine*, *change* and *compare*. Word problems with the same arithmetic solution but belonging to different semantic types, yields different degrees of difficulties and types of errors.

We investigated the relation between problem difficulty based on semantic structure of the problem and the ability of different achievement groups to choose the symbolic problem which can answer the word problem. The research question was: Do low performers more often choose an incorrect symbolic problem on semantic difficult word problems than other students do? The paper and pencil test included 75 (64 selected for analysis) multiple-choice items of word problems with four options (one correct). Example: “5 students were supposed to perform together, but 2 students had not practiced. How many students had practiced?” Options: 2 – 5; 5 – 2; 3 + 2; 5 : 2. The word problems were carefully constructed to cover the different semantic structures within each of the four operations with both single digit and multi digit numbers. Each item was categorized as ‘easy’ (straightforward to solve) or ‘difficult’ (less straightforward) based on semantic structure. E.g. for addition, *combine* and *change* was categorized as easy, whereas *comparison* and *change after a reduction* was categorized as difficult. 1081 students (86 classes, 31 schools) from 3^{rd} to 6^{th} grade participated. The students’ teacher scored their general mathematics performance (1 to 5).

**Analysis, results, discussion and implications**

We used a multi-level analysis with item as observation unit, correct answer as opposed to incorrect/no answer as a binary response variable and student-ID as random effect. Fixed effects were grade (covariate), teacher’s assessment score (categorical), item difficulty (easy vs. difficult) and the interaction between item difficulty and assessment score. We modelled addition problems (14 items), division problems (13 items), multiplication problems (14 items) and subtraction problems (23 items) separately.

The proportion of correct answers were higher for addition problems than for the other arithmetic operations. For all four operations, the proportion of correct answers increased with grade and assessment score and decreased with level of difficulty (all p < 0.001). Significant interaction between level of difficulty and assessment score only existed for addition problems: low performing students performed disproportionately worse on ‘difficult’ items compared to high performing students. Hence, for addition problems, difference in ability to choose correct symbolic problem between low and high performing students partly relates to the difficulty/complexity of the problem, while it for other arithmetic operations relates to the operation type itself. Roughly speaking, low performers only recognize straightforward addition word problems.

It is important to support all students’ development of the understanding that multiple types of situations can be expressed by the same calculation and vice versa. We suggest an increased focus on teaching adaptive flexible strategies and the process of matching a symbolic problem to a word problem and not only on solving the problem or performing the calculation.

### References

Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. *ZDM, 52*(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4

## Paper 3: Adapting mathematics teaching to diverse learners needs

**Jónína Garðarsdóttir, Glerárskóli, Akureyri, joninaga@glerarskoli.is**

### Abstract

Supporting students who face difficulties in learning mathematics and help them increase their mathematical competences can be challenging for teachers. Students who repeatedly have experienced frustration often believe that mathematics is a subject that can only be mastered by some but not by others. They think that they do not have what it takes to become good at mathematics and that their study of the field is meaningless (Boaler, 2016; Bishop og Kalogeropoulos, 2015).

The purpose of this study is to increase the knowledge and understanding of how teachers in Iceland meet the challenges of teaching mathematics in inclusive schools. Particularly the goal is to learn about teachers’ experience of working with students who struggle with mathematics. Research question: How do teachers experience working with students who face difficulties in learning mathematics?

A phenomenological approach, the Vancouver School, was chosen to answer this question as such methods are intended to provide an increased understanding of human phenomena (Halldórsdóttir, 2000). Eight teachers participated in the study and they were interviewed on the basis of an open questionnaire.

The main findings were that the teachers approach their teaching in diverse ways. They emphasized finding ways to support every student according to their needs.

**Four main themes emerged:**

a) Students who find mathematics learning difficult are often taught in a separate room as this suits their needs.

b) Students who find mathematics learning difficult enjoy finding their own solution strategies and it supports their learning. This also applies to working with students with diverse competence in mathematics.

c) Most special needs students work with the same textbook as their classmates.

d) Teachers who teach students who find mathematics learning difficult emphasize well-being.

The main conclusions were that teachers found that traditional teaching methods dominated mathematics teaching in their schools and they found it difficult to adapt their teaching to more creative approach. Introducing the latest research findings on mathematics teaching and learning needs to be introduced to the school community. It needs to reach students, parents, teachers, headmasters and others, who are responsible for mathematics teaching and learning at school.

### References

Boaler, J. (2016). *Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching*. San Francisco: Jossey-Bass & Pfeiffer Imprints.

Bishop, A. J. og Kalogeropoulos, P. (2015). (Dis)engagement and exclusion in mathematics. In Alan Bishop, Hazel Tan, Tasos N Barkatsas (eds.), *Diversity in mathematics education: Towards inclusive practices. *(pp. 193–218). Cham: Springer International Publishing.

Halldórsdóttir, S. (2000). The Vancouver School of doing phenomenology. In B. Fridlund og C. Hildingh (eds.), *Qualitative research methods in the service of health *(pp. 47–81). Lund: Studentlitteratur.