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The Xmanian number system uses letters like A, B, C to represent quantities and values in a unique counting system. Numbers are formed by combining letters in a consistent pattern, such as A0, A1, AA, AB, up through combinations of four letters. The document asks the reader to consider what advantages and disadvantages this unusual letter-based numbering system might have.
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Intro xmania counting
The Xmanians had a problem with their number system as it only went up to the letter Z and collections larger than that were described as "many". Mathematicians set out to create a new number system and presented their ideas at a conference. The most promising system used the symbols 0, A, B, C, and D and could count infinitely high while specifying exact quantities. Unfortunately, the creator of this system disappeared before revealing it, but left clues that students are tasked with piecing together to reconstruct the missing number system.
Dr. Robert Berry
This document discusses the experiences of Black boys who are successful in mathematics. It begins by explaining the need to change the narrative around Black boys from one of deficiency to one of success. It then provides an overview of research on Black students in mathematics from the 1970s to present, which has transitioned from a focus on achievement gaps to opportunities and complex factors impacting experiences. The remainder of the document tells the story of Bilal, a Black male student who was successful in mathematics from middle school through college, though he still faced challenges with race, identity, and confidence at times.
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1) The document describes a professional development program called Project AIM that teaches elementary school teachers strategies to promote productive mathematical discourse in their classrooms.
2) One strategy discussed is called "Bet Lines", adapted from literacy education, where students make predictions about what will happen next in a word problem. When used correctly, this strategy engages students and elicits their prior knowledge to motivate engagement with the task.
3) A video example shows a teacher successfully using Bet Lines to launch a lesson, with students making predictions about the problem and quantities involved. The strategy prepares students for problem-solving and discourse.
Dr. Paola Sztajn AM talk
This document summarizes two studies examining research on mathematics teacher professional development (PD). The first study by Yoon and Sztajn reviewed PD research from 1992 to 2010 to analyze how PD interventions were described. The second study by Sztajn, Borko, and Smith reviewed research from 2005 to 2014 to provide an overview of the field and what is known about the impact, scale, and comparisons of different mathematics PD programs. Both studies aimed to better understand PD "inputs" in addition to typical focuses only on "outcomes".
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This document discusses intentional communities for learning together to lead productive mathematical discussions. It begins by acknowledging that children have amazing ways of solving problems and that knowing how to respond to students' ideas and facilitate meaningful discussions can be both invigorating and challenging. It then provides principles for supporting discussion, such as ensuring students know what to share and that their ideas are valued.
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Intro xmania counting
The Xmanians had a problem with their number system as it only went up to the letter Z and collections larger than that were described as "many". Mathematicians set out to create a new number system and presented their ideas at a conference. The most promising system used the symbols 0, A, B, C, and D and could count infinitely high while specifying exact quantities. Unfortunately, the creator of this system disappeared before revealing it, but left clues that students are tasked with piecing together to reconstruct the missing number system.
Dr. Robert Berry
This document discusses the experiences of Black boys who are successful in mathematics. It begins by explaining the need to change the narrative around Black boys from one of deficiency to one of success. It then provides an overview of research on Black students in mathematics from the 1970s to present, which has transitioned from a focus on achievement gaps to opportunities and complex factors impacting experiences. The remainder of the document tells the story of Bilal, a Black male student who was successful in mathematics from middle school through college, though he still faced challenges with race, identity, and confidence at times.
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1) The document describes a professional development program called Project AIM that teaches elementary school teachers strategies to promote productive mathematical discourse in their classrooms.
2) One strategy discussed is called "Bet Lines", adapted from literacy education, where students make predictions about what will happen next in a word problem. When used correctly, this strategy engages students and elicits their prior knowledge to motivate engagement with the task.
3) A video example shows a teacher successfully using Bet Lines to launch a lesson, with students making predictions about the problem and quantities involved. The strategy prepares students for problem-solving and discourse.
Dr. Paola Sztajn AM talk
This document summarizes two studies examining research on mathematics teacher professional development (PD). The first study by Yoon and Sztajn reviewed PD research from 1992 to 2010 to analyze how PD interventions were described. The second study by Sztajn, Borko, and Smith reviewed research from 2005 to 2014 to provide an overview of the field and what is known about the impact, scale, and comparisons of different mathematics PD programs. Both studies aimed to better understand PD "inputs" in addition to typical focuses only on "outcomes".
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It distinguishes between open strategy sharing, where many different ideas and strategies are elicited, and targeted sharing, where the discussion is focused on a particular strategy or mathematical idea. Examples of both types of discussions are provided. Targeted structures like "Why? Let's Justify" are outlined to generate justifications for strategies. The document concludes by discussing learning
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The document describes the design of a teacher education program that uses rehearsals to help novice teachers learn ambitious pedagogies. The program pairs a university math methods course with placements in an elementary school, where teachers-in-training plan lessons, rehearse teaching activities, and receive feedback. Rehearsals last 12-15 minutes and allow novices to practice instructional techniques in a supportive environment. The program aims to bridge the gap between learning about teaching and actual classroom practice through structured learning cycles and a focus on core teaching practices.
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This document summarizes a presentation about preparing elementary school teachers to understand elementary mathematics. It discusses how elementary mathematics concepts can be complex and how focusing on children's mathematical thinking can help prospective teachers (PSTs) engage more deeply with mathematics. The presentation addresses four principles: 1) How students typically learn mathematics is problematic, 2) Learning concepts is more powerful than procedures, 3) Students' reasoning is varied and complex, and 4) Elementary math is not as elementary as assumed. Research found PSTs who learned about children's thinking improved their math knowledge and developed more sophisticated beliefs than those who did not.
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The document discusses a presentation about the nature of teacher knowledge, specifically specialized content knowledge (SCK) which is knowledge used for teaching but not directly taught to students. It describes research assessing SCK among different groups like prospective teachers and more experienced teachers, finding that SCK increases with experience. The presentation also discusses goals for further research on developing teachers' SCK, especially regarding integers and students' reasoning about them.
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Summary new xmania_counting
- 2. Xmania uses SOME letters to name quantities: A B C AND counting is done….
- 4. A
- 5. B
- 6. C
- 7. D
- 8. A0
- 9. A0
- 10. AA
- 11. AB
- 12. AC
- 13. AD
- 14. B0
- 15. B0
- 16. BA
- 17. BB
- 18. BC
- 19. BD
- 20. C0
- 21. C0
- 22. CA
- 23. CB
- 24. CC
- 25. CD
- 26. D0
- 27. D0
- 28. DA
- 29. DB
- 30. DC
- 31. DD
- 32. A00
- 33. A00
- 34. A00
- 35. ACC
- 36. ACC
- 37. Think about what might be the advantages of this system? Disadvantages?