The document discusses the history and development of Hindu-Arabic numerals. It originated in India in around 300 BC and was developed by a mathematician named al-Binuri. These numerals evolved and spread to the Middle East and Europe through Arab traders in the 10th century. Leonardo Fibonacci helped popularize the use of Hindu-Arabic numerals in Europe in the early 13th century through his book Liber Abaci, as they were more efficient than traditional Roman numerals. Today, the Hindu-Arabic numeral system with 10 symbols (0-9) is the most widely used numeral system globally.
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.
The document discusses the history and development of Hindu-Arabic numerals. It originated in India in around 300 BC and was developed by a mathematician named al-Binuri. These numerals evolved and spread to the Middle East and Europe through Arab traders in the 10th century. Leonardo Fibonacci helped popularize the use of Hindu-Arabic numerals in Europe in the early 13th century through his book Liber Abaci, as they were more efficient than traditional Roman numerals. Today, the Hindu-Arabic numeral system with 10 symbols (0-9) is the most widely used numeral system globally.
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 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.
5. Sytten, atten, nitten, titten... Det er i butikken like før jul og en jente på 4-5 år skal hjelpe til med å kjøpe mandariner. Hun putter en og en i posen mens hun teller: «En, to, tre, ... sytten, atten, nitten, titten!»
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9. Barn og parkobling I en førsteklasse er det en dag bare 18 av i alt 24 elever tilstede. Rukshana (lærer) utnytter situasjonen til matematikk: «Hvor mange mangler vi?» «Seks!» «Hvordan fant du ut det?» «Jeg bare telte de tomme stolene!»
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12. Johanne, 6 år, spiller fremdeles sitt selvlagede terningspill. I stedet for bamsen har hun imidlertid fått en voksen medspiller. Johanne noterer prikker på arket akkurat som sist, men nå er hun ikke lenger fornøyd med å anslå vinneren. Nå vil hun gjerne både telle opp poengene og skrive ned riktig resultat. Etter hvert som antall prikker på arket stiger, går Johanne lett surr når hun skal telle opp poengene, hun glemmer prikker eller teller noen to ganger. Den voksne vet at Johanne kan telle tiere og foreslår at hun i stedet for å telle en og en, først skal telle sammen ti og ti og markere det med en strek eller en ring. Og grupperingen rydder opp for Johanne, nå finner hun poengsummen uten problemer.