Syftet med denna studie var att beskriva olika arbetssätt som lärare använder i sin matematikundervisning, och vilka faktorer som vissa lärare anser styr vilka arbetssätt de väljer att arbeta med, samt att visa på hur vissa lärare anser att de har ändrat sin undervisning sedan de deltagit i Matematiksatsningen, som är en satsning från regeringen att förbättra matematikundervisningen, eller under sin tid som lärare. I den teoretiska bakgrunden beskrivs ramfaktorteorin, vilket är yttre faktorer som kan påverka skolan som organisation, exempelvis i form av tidsfördelning, klasstorlek och andra ekonomiska resurser. Jag beskriver också den sociokulturella teorin och hur Piaget och Vygotskij beskriver barns olika intelligensnivåer. Undersökningens datainsamling skedde i form av kvalitativ halvstrukturerad intervju, där jag utgick från en intervjuguide med frågor för att ta reda på vilka arbetssätt dessa lärare säger sig arbeta med och vilka faktorer de anser påverkar deras val av arbetssätt. Samt hur de anser att Matematiklyftet har påverkat deras sätt att undervisa och hur de anser att de har ändrat sin undervisning under tiden som lärare. Resultatet av intervjuerna kan kort sammanfattas att de intervjuade lärarna arbetar med många arbetssätt men i olika utsträckning, och att faktorer som påverkar valet av arbetssätt också ser olika ut, i stora drag nämner de faktorer som gruppstorlek, gruppsammansättning, miljö och material. De intervjuade lärarna beskriver också att de under sin tid som lärare och framförallt efter Matematiklyftet har dragit ner på drillövningar och istället jobbar mer med problemlösninguppgifter. / The purpose of this study is to describe the different working methods that teachers use in their teaching of mathematics, and the factors that some teachers believe effect the choice of their working methods.  The interviewed teachers also describe how they think that they have changed their teaching since they participated in Math Initiative, which is an effort to improve mathematics education from the government, or their time as teachers.   In the theoretical background I describe ramfaktorteorin, which are external factors that can affect the school as an organization, such as scheduling, class size and other economic resources.  I also describe the socio-cultural theory and how Piaget and Vygotskij describes children's different levels of intelligence.   I collected data for my thesis in the form of qualitative semi-structured interview, which was based on an interview guide. With these questions I wanted to find out what different work methods these teachers say they use in their teaching in mathematics. What factors do they believe affect their choice of working methods? And how they think that Mathematics Initiative has affected their way of teaching and how they believe that they have changed their teaching during their time as a teacher. The result of the interviews can be summarized that the interviewed teachers work with many different working methods in very varying degrees, and the factors that affect the choice of working methods also varying, they mention factors  group size, group composition, environment and materials. The interviewed teachers also describes that during their time as a teacher and especially after the Mathematics Initiative they have drawn down on drill exercises and instead work more with problem-solving tasks.

Genom att lyfta kommunikation som verktyg i matematisk problemlösning kan elevers möjlighet till måluppfyllelse öka. Kommunikation mellan elever i grundskolans senare år synliggörs i denna studie som även vill ge svar på i vilka former kommunikation visar sig. Eleverna arbetade med arbetsmetoden eget, par, alla (EPA) som rekommenderas av skolverket, samt bra, bättre, bäst metoden (BBB). Metoden utvecklades i ett aktionsforskningsprojekt som pågick 2016 till 2017 i samarbete mellan Norrköping och Linköpingsuniversitet. En forskningsgrupp utvecklade ett arbetssätt som eleverna namngav bra, bättre, bäst metoden, vilken inkluderar en nätbaserad uppgiftsbank som baseras på elevarbeten. Denna studie innefattar enskilda intervjuer med 16 elever. Därtill digitalinspelades 76 elever under matematiskt problemlösningsarbete där fenomenografisk analysmetod genomfördes. Resultatet visade att kommunikationsutbytet mellan eleverna varierade beroende på vilken arbetsmetod som användes, samt att elevernas olika kunskapsnivåer inte märkbart påverkade den kommunikation som framkom under gruppsamarbetet. Studien visar att gruppernas uppbyggnad är en viktig faktor för att höja kvalitén i elevernas arbeten.

Educational games intend to make learning more enjoyable, but at the potential cost of compromising learning efficiency. Therefore, instead of creating educational games, we create learning environment with game-like elements: the elements of games that are engaging. Our approach is to assess each game-like element in terms of benefits such as enhancing engagement as well as its costs such as sensory or working memory overload, with a goal of maximizing both engagement and learning. We developed different four versions of a math tutor with different degree of being game-like such as adding narrative and visual feedback. Based on a study with 297 students, we found that students reported more satisfaction with more 'game-like' tutor but we were not able to detect any conclusive difference in learning among the different tutors. We collected student data of various types such as their attitude and enjoyment via surveys, performance within tutor via logging, and learning as measured by a pre/post-test. We created a causal model using software TETRAD and contrast the causal modeling approach to the results we achieve with traditional approaches such as correlation matrix and multiple regression. Relative to traditional approaches, we found that causal modeling did a better job at detecting and representing spurious association, and direct and indirect effects within variables. Causal model, augmented with domain knowledge about likely causal relationships, resulted in much more plausible and interpretable model. We propose a framework for blending exploratory results from causal modeling with randomized controlled studies to validate hypotheses.

Course grades, which often include non-achievement factors such as effort and behavior and are subject to individual teacher grading philosophies, suffer from issues of unreliability. Yet, course grades continue to be utilized as a primary tool for reporting academic achievement to students and parents and are used by most colleges and universities as an admissions measure. High-stakes assessment results are also used by schools to convey student achievement, and several states now require students to pass an exam to receive a diploma. What is less clear, however, is the relation between these two measures, GPA and high-stakes assessment results. One purpose of this study was to examine the predictive relation of mathematics GPA to student performance on high-stakes assessments. Multiple regression models were used to analyze the predictive relation between mathematics GPA and performance on the ACT and the Oregon Assessment of Knowledge and Skills (OAKS), two high-stakes assessments. In addition, the regression analyses were used to examine the influence of other student-level variables such as talented and gifted status and math courses taken prior to testing on the relation between mathematics GPA and performance on the two high-stakes assessments. In all, 299 high school students from a single grade-level enrolled in one Oregon suburban school district participated in the study. Results indicate that GPA is a significant variable in a high-stakes assessment outcome. Additionally, results of the multiple regression reveal significant student-level effects on assessment outcomes that reduce explained common variance in both the ACT and OAKS models. Implications for practice and suggestions for future research are discussed.

The purpose of this study was to determine the effectiveness of a video-based instruction packet as a method of teaching math-based vocational skills delivered through augmented reality to three adults with intellectual disabilities. The dependent variable was the percentage of steps performed correctly to solve each selected type of math problem. The independent variable was the video-based math intervention delivered via augmented reality, which modeled the individual steps for solving three different multi-step math problems: (1) adjusting a recipe to serve a different number of people, (2) calculation of salary, (3) calculation of unit prices. Visual and statistical analysis demonstrated a functional relationship between the video-based math intervention and an increase in the percentage of steps completed correctly for each type of problem. All three participants showed significant gains immediately after receiving the intervention and maintained the learned skills even following the withdrawal of the intervention. Implications for practitioners and further research are discussed.

For this session, we will higlight project-based learning (PBL) as a method for integrating science, math, and literacy while addressing state curriculum standards for each subject area. PBLs prompt students to interact with science, math, and literacy in a way that enhances the connection between all three subject areas and provides a real-world context for learning. In this session, we will provide ideas and strategies to begin developing PBLs for your classroom and share example PBLs that integrate math, science, and literacy at the middle school level.

Learn how to use Lego sets to promote math content and practices.

Let R(G) denote the category of smooth representations of a p-adic group. Bernstein has constructed an indexing set B(G) such that R(G) decomposes into a direct sum over s ∈ B(G) of full subcategories Rs(G) known as Bernstein subcategories. Bushnell and Kutzko have developed a method to study the representations contained in a given subcategory. One attempts to associate to that subcategory a smooth irreducible representation (τ,W) of a compact open subgroup J < G. If the functor V ↦ HomJ(W,V) is an equivalence of categories from Rs(G) → H(G,τ)mod we call (J,τ) a type. Given a Levi subgroup L < G and a type (JL, τL) for a subcategory of representations on L, Bushnell and Kutzko further show that one can construct a type on G that “lies over” (JL, τL) by constructing an object known as a cover. In particular, a cover implements induction of H(L,τL)-modules in a manner compatible with parabolic induction of L-representations. In this thesis I construct a cover for certain representations of the Siegel Levi subgroup of Sp(2k) over an archimedean local field of characteristic zero. In partic- ular, the representations I consider are twisted by highly ramified characters. This compliments work of Bushnell, Goldberg, and Stevens on covers in the self-dual case. My construction is quite concrete, and I also show that the cover I construct has a useful property known as splitness. In fact, I prove a fairly general theorem characterizing when covers are split.

The goal of this study was to examine the impact of exercising while completing an academic task on performance on the academic tasks. Participants were 71 undergraduate students at a midsized southern university who were asked to complete reading and math tasks while exercising on a stationary bike. Performance on reading and math tasks completed on the stationary bike was compared within-subjects to performance on parallel tasks while seated. Working memory scores were assessed as potential covariates. Order of experimental tasks was evaluated as a between-subjects factor. Within-subjects ANCOVA’s indicated that performance on math tasks was significantly worse while exercising. However, no significant differences were found between reading tasks completed while seated and reading tasks completed while exercising. Working memory scores were not significant covariates, and order of experimental tasks was not a significant between-subjects factor. Cognitive load differences were assessed for the different experimental tasks. It is believed that variation in cognitive load during different experimental tasks explains the differences in the reading and math results. The findings of this study indicate that future research should focus on varying the difficulty of the tasks.

Low math achievement among elementary school students is a concern because students who lack a strong early foundation in mathematics may experience difficulty learning in future mathematics classes. Students in 2 rural southeastern school districts demonstrated low math achievement in 5th grade and their scores declined from 3rd to 5th grade. In this quantitative study, teacher-related factors that research has shown to predict student achievement were examined using Bandura's theory of self-efficacy and Ball and McDiarmid's emerging theory of subject matter content knowledge. The research question asked whether the teacher factors, years of teaching experience, hours of professional development in math pedagogy, college math courses completed, math teacher preparation courses, and teaching efficacy, predicted student math achievement in the 2 districts. Data were collected from 29 3rd grade teachers and 32 5th grade teachers and analyzed using binary logistic regression. The findings showed that the combination of predictors did not significantly predict math achievement of 5th grade students. However, teachers who had 1 to 9 years of teaching experience were more likely to have students with higher math achievement than those with more than 20 years of experience (OR = 4.96; p = .048). The inconclusive results indicate that additional factors that might influence students' math achievement have to be explored and additional professional development has to be offered, especially for teachers who have been teaching for 2 decades as they might have learned curriculum and pedagogy different from current practice. Positive social change will occur when all elementary teachers are able to facilitate students' learning of mathematics and the students successfully master math concepts.