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數學的閱讀理解與教學

數學的閱讀理解與教學. 學生數學沒學好的原因是什麼. 國外老師認為.

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數學的閱讀理解與教學

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  1. 數學的閱讀理解與教學

  2. 學生數學沒學好的原因是什麼

  3. 國外老師認為 When a student is not successful in math, teachers usually assume the difficulty is with the student’s mathematical ability or possibly the student’s dislike of mathematics, but the truth may more likely lie with the student’s poor ability to read the mathematics textbook. (Draper, Smith, Hall, & Siebert, 2005; Kane, Byrne, & Hater, 1974; O’Mara, 1982)

  4. 學生在數學課中的學習經驗 • 和教科書的關係是 • 對老師的期待是 • 學習數學最好的方法是

  5. Students’ Common Experiences In Math Classrooms • Students find math textbooks to be intimidating and confusing and therefore just skip past the explanations. (Draper, 1997) • Students expect the teacher to be the expert, do all the talking, and be the center of the classroom. • Students say the best means of learning math are (Stodolsky, Salk, & Glaessner, 1991) • “hearing an explanation” • “asking someone” • “being told what to do”

  6. 教師在數學課中的教學經驗 • 對學生閱讀能力差的想法是 • 在教科書和學生間的角色是

  7. Teachers’ Common ExperiencesIn Math Classrooms • Teachers compensate for students’ lack of reading ability by using the textbook as a resource for exercises only. (Draper, 2002; Porras, 1994) • Teachers “tell” students all necessary information therefore releasing students from needing to read the textbook. (Draper, 2002; Porras, 1994)

  8. 你認為 • 閱讀數學和閱讀其它學科的能力一樣嗎？ • 在別的學科可以學到閱讀數學的能力嗎？ • 數學文本特別之處為何？ • 學生如何使用教科書呢？

  9. Reading in Math(Barton & Heidema, 2002) • Mathematics texts contains more concepts per word, per sentence, and per paragraph than other text • Writers of mathematics texts generally write in a very terse or compact style • In K-12, math textbooks are often written above grade level. • Overlap between math and everyday English vocabulary can cause confusion.

  10. Reading in Math (Barton & Heidema, 2002) • Reading mathematics is not always from left to right • Requires unique knowledge and skills not taught in other content areas. • Students need to be proficient at decoding words, numbers, and symbols. • Students often skip over the worded parts looking for examples, graphics, or exercises.

  11. 你認為 • 數學語言為什麼不易理解？ • 一種表徵有多種意義，但需在脈絡中給予正確理解 • 讀音和意義不合，或有類似的讀音 • 對偶性的概念

  12. The Math Register and Vocabulary(Rubenstein, 2007) • Some words… • have multiple meanings in math (e.g., point, cube, range) • Sound like other words (e.g., sum & some, plane & plain, intercept & intersect, complement & compliment, hundreds & hundredths, pie & pi) • are learned in pairs that often confuse students (e.g., complement & supplement, combination & permutation, solve & simplify, at most & at least)

  13. 還有呢？ • Certain concepts in mathematics are embedded within other concepts to be defined and understood. • Three categories of math words • Words that have the same meaning in Mathematical English (ME) and Ordinary English (OE) • Words that have meaning only in ME • Words that have different meanings in ME and in OE

  14. 閱讀理解教學 • 閱讀理解的教學目標是什麼？ • 教閱讀理解的好處是什麼？

  15. Easy Additions to Instruction • Research shows… • 理解文本特徵有助於閱讀理解 • 連結至先備知識有助於閱讀理解 • 恰當的閱讀策略有助於閱讀理解

  16. 閱讀策略的教學範例 • 概念定義 • 專有名詞 • 解題 • 教學生閱讀

  17. 動動腦、做做看 • What vocabulary difficulties could students have? • What do you think they may find confusing? • Are the explanations well written? • What is left unexplained? • Do you only read from left-to-right and from top-to-bottom? • What isn’t defined that you think should be? • Do they know how to read the graph and how to connect it to the other information given?

  18. Textbook Use(Daniels & Zemelman, 2004) • Remind the students about what they already know – prior knowledge. • Research shows that students find it very difficult to learn from the math textbook with little or no support from their teacher. • Research shows a strong connection between vocabulary knowledge and the ability to understand what is read. • Be explicit about the what, why, and how for each strategy shown to your students.

  19. Final Thoughts • “A mathematics education that assumes to prepare students without providing them with ways to access the text falls short of truly educating students” (Draper, 2002). • “The priority of instructing for reading comprehension must be balanced with the priority of teaching the content area itself” (RAND, 2002, p. 30).

  20. 提問與討論

  21. References • Barton, Mary Lee & Heidema, Clare. 2002. Teaching Reading in Mathematics. Colorado: MCREL • Billmeyer, Rachel & Barton, Mary Lee. 2002. Teaching Reading in the Content Areas: If Not Me, Then Who? Alexandria: ASCD • Harvey, Stephanie & Goudvis, Anne. 2000. Strategies That Work. Ontario: Stenhouse Publishers. • Tovani, Cris. 2000. I Read It, But I Don’t Get It. Maine: Stenhouse Publishers

  22. Example of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002) Definition (in own words) Facts/Characteristics WORD or SYMBOL Non-Examples Examples

  23. Example of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002) Definition (in own words) Facts/Characteristics An expression in this form is called a radical, b is called the radicand and the n is called the index of the radical. is the positive square root of a is the negative square root of a RADICAL Non-Examples Examples

  24. Example of a Vocabulary StrategyFrayer Model – (Barton & Heidema, 2002) Facts/Characteristics Definition (in your own words) *there is never an index=1 *odd roots are always the same sign as the number under the radical. These are radical signs . When no superscript number is in front (called the index) it means it is square root. With a “3” index it becomes a cube root and so on. or Non-Examples Examples Not a radical – this is a division sign

  25. Example of a Vocabulary StrategyVerbal and Visual Word Association – (Barton & Heidema, 2002) Vocabulary Term(s) Visual Representation Personal Association or a characteristic Definition(s)

  26. Example of a Vocabulary StrategyVerbal and Visual Word Association – (Barton & Heidema, 2002) Root, Zero, Factor, Solution, x-intercept x= -2 x= 3 x-axis Each word can represent the answer to the function y=f(x) where f(a)=0 and a is a root, zero, factor, solution, and x-intercept -Point (a,0) is the x-intercept of the graph of y=f(x) -number a is a zero of the function f -number a is a solution of f(x)=0 -(x-a) is a factor of polynomial f(x) -Root is the function on the TI for this y-axis f(x) Just find the answer to the function and that will be the zero. If I graph it, the zeros are where the function crosses the x-axis. Special Note: this is just for real solutions.

  27. What is it Like? What is it? The Word > What are Some Examples?

  28. What is it Like? What is it? The Word > Closed Mathematical Shape Plane Figure Polygon Straight Sides Two-Dimensional Pentagon Hexagon Rhombus Made of line segments What are Some Examples?

  29. K-N-W-S

  30. Use Jigsaw to Encourage Reading • When teaching quadratic solution methods… • 分組討論，每組閱讀課本討論一種方法, • 重新分組，讓每一組都有不同方法的成員 • 成員中互相解釋釐清各種方法 • 各組內討論各種方法的優缺點 • 互相評論與賞析

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