This document discusses a study on teachers' epistemic beliefs about mathematical knowledge for teaching definitions. The study involved focus group interviews with 15 teachers discussing their reflections on MKT items. The results showed that while teachers felt knowing definitions was important, they did not think remembering the exact definitions was as important. Teachers also felt definitions were more critical in higher grades and that exact definitions could confuse students. The conclusions were that teachers see value in conceptual knowledge of definitions but not rote memorization of definitions.
This is a presentation of our project related to MKT (mathematical knowledge for teaching) in Stavanger. The presentation was held by Arne Jakobsen at the University of Algarve, June 1st 2011.
1) The document analyzes correlations between teachers' mathematical knowledge for teaching (MKT) scores in different content areas including number concepts and operations (NCOP), geometry, and patterns, functions and algebra (PFA).
2) It finds that teachers' MKT scores in the three content areas are positively correlated, with the weakest correlation between PFA and NCOP.
3) While teachers commented that some content areas like PFA were not relevant to their teaching, their PFA MKT scores were still related to their MKT scores in other content areas.
This document summarizes presentations from a conference on adapting and using measures of mathematical knowledge for teaching (MKT) developed in the United States for use in other countries. It discusses challenges in translating MKT items for use in Norway, validating an adapted Korean version of the MKT, translating MKT geometry measures for Indonesia, examining relationships between MKT scores and the mathematical quality of instruction in Ghana for three teachers, and using qualitative and quantitative methods to study the equivalence of the teacher knowledge construct across countries.
This document discusses developing teachers' abilities to facilitate mathematical learning in kindergarten students. It outlines a research project using learning studies and variation theory to help teachers discern how students understand change and stability in math concepts. The project will collaborate between Sweden, Finland, and Norway, using learning studies to explore kindergarten teachers' mathematical knowledge for teaching. The goal is to help teachers better understand students' preconceptions and plan lessons that utilize variations to improve learning.
This document discusses a study on teachers' epistemic beliefs about mathematical knowledge for teaching definitions. The study involved focus group interviews with 15 teachers discussing their reflections on MKT items. The results showed that while teachers felt knowing definitions was important, they did not think remembering the exact definitions was as important. Teachers also felt definitions were more critical in higher grades and that exact definitions could confuse students. The conclusions were that teachers see value in conceptual knowledge of definitions but not rote memorization of definitions.
This is a presentation of our project related to MKT (mathematical knowledge for teaching) in Stavanger. The presentation was held by Arne Jakobsen at the University of Algarve, June 1st 2011.
1) The document analyzes correlations between teachers' mathematical knowledge for teaching (MKT) scores in different content areas including number concepts and operations (NCOP), geometry, and patterns, functions and algebra (PFA).
2) It finds that teachers' MKT scores in the three content areas are positively correlated, with the weakest correlation between PFA and NCOP.
3) While teachers commented that some content areas like PFA were not relevant to their teaching, their PFA MKT scores were still related to their MKT scores in other content areas.
This document summarizes presentations from a conference on adapting and using measures of mathematical knowledge for teaching (MKT) developed in the United States for use in other countries. It discusses challenges in translating MKT items for use in Norway, validating an adapted Korean version of the MKT, translating MKT geometry measures for Indonesia, examining relationships between MKT scores and the mathematical quality of instruction in Ghana for three teachers, and using qualitative and quantitative methods to study the equivalence of the teacher knowledge construct across countries.
This document discusses developing teachers' abilities to facilitate mathematical learning in kindergarten students. It outlines a research project using learning studies and variation theory to help teachers discern how students understand change and stability in math concepts. The project will collaborate between Sweden, Finland, and Norway, using learning studies to explore kindergarten teachers' mathematical knowledge for teaching. The goal is to help teachers better understand students' preconceptions and plan lessons that utilize variations to improve learning.
17. Du vet hva trekant, firkant og femkant er. Men hvordan ser en tokant ut? Og hva med en énkant, eller nullkant? Er det kanter eller hjørner som avgjør? Er en kant nødvendigvis rett? Kan en åpen figur være en trekant?
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19. Utforsking i lek Jo (3 ½ år) kopierer et mønster med plastbrikker. Mønsteret er bygget opp av trekanter og kvadrater i ulike farger. Etter en stund er det ikke flere røde kvadrater igjen og Jo er rådvill. Hvordan komme videre? Førskolelæreren viser at han kan lage et kvadrat ved å legge to røde trekanter inntil hverandre. Jo prøver selv. Tar to røde trekanter – det stemmer. Mønsteret fortsetter. Det neste skal være et blått kvadrat. Han ser på brikkene, finner to blå trekanter – det blir også et kvadrat! Jo haster videre, han er ikke lenger opptatt av de kvadratiske brikkene. Hver gang det dukker opp et kvadrat i mønsteret, finner han fram to trekanter i passende farge.
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26. Hull... «Hva var det som hendte?» spurte Brumm. «Hvor er vi?» «Jeg tror vi er i et slags hull,» sa Nøff. «Jeg gikk bortover og lette etter noe og plutselig var jeg der ikke mer...»