CURRICULUM AND TEACHING-- SECONDARY MATHEMATICS … Curriculum and Teaching Math_tcm1… · ( ......

1

CURRICULUM AND TEACHING-- SECONDARY MATHEMATICS

Fall 2013 02.575/201

Thursdays 4:00-6:30 pm

Instructor: Dr. Roser Giné

Office Hours: Mondays, 8:30-10:00 am, Tuesdays, 10:00 am -11:30 pm, or by appointment

Office: OL 533 e-mail: [email protected]

Phone: (978) 934-4355

COURSE OVERVIEW/RATIONALE

This course is designed to introduce prospective mathematics teachers to curriculum design and teaching approaches that are research-based and address the needs of a diverse population of students.

Through various course assignments, students will:

§ Understand aspects of their own mathematical thinking

§ Explore and analyze critical ways of thinking mathematically

§ Use an evolving understanding of mathematics and mathematical thinking in order to guide secondary school students towards their construction of essential mathematical ideas

§ Analyze current issues in mathematics education that impact teaching and learning in schools

§ Experience and analyze various mathematics curricula, with a focus on relevant reform initiatives

2

§ Explore and implement the Massachusetts Common Core State Standards for Mathematics by designing lessons and units that engage students in important mathematical practices identified in the practice standards

GRADUATE SCHOOL OF EDUCATION CONCEPTUAL FRAMEWORK

A theme entitled Education for Transformation provides a conceptual framework that unifies programs at the Graduate School of Education. The mission of the University of Massachusetts Lowell is to promote and sustain regional economic development. The Graduate School of Education (GSE) contributes to this mission by developing professionals who help transform the region through leadership roles in education. The GSE’s commitment to “Education for Transformation” produces graduates who:

• Demonstrate excellent knowledge, judgment, and skills in their professional fields; • Promote equity of educational opportunity for all learners; • Collaborate with other educators, parents, and community representatives to support

educational excellence; • Use inquiry and research to address educational challenges

The fundamental tenets of the school are excellence, equity, collaboration and inquiry. Your Role in Education for Transformation As a new teacher you are expected to use the knowledge and hone the skills and dispositions needed for excellence in teaching. In this way you have the opportunity to be part of a cadre of professionals graduating from UML who become leaders in their schools and show commitment to their school and community.

3

REQUIRED MATERIALS

Required Readings by Class Session:

To be read before…

Article(s)

Sept. 12, 2013

Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. (can be downloaded as a pdf from Google Scholar)

Common Core Standards for Massachusetts—Review Practice Standards on pp. 15-17 (http://www.doe.mass.edu/candi/commoncore/ )

Sept. 19, 2013

Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40, 259-281. (can be downloaded as a pdf from Google Scholar)

Giné, R. & Kruse, D. (2007). What if less is just less? The Role of depth over breadth in the secondary mathematics curriculum. Horace, 23(2), 5-15. Can be downloaded at: http://www.essentialschools.org/resources/383 Wiggins & McTighe: Understanding by Design (excerpt and template will be handed out in class)

Sept. 26, 2013

Cuoco, A. et al. (1996). Habits of Mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375-402. (will be handed out in class or posted on Blackboard)

CME mathematics unit for review (will be handed out in class)

Smith, M. & M.K. Stein (2010). The Role of Curricular Materials in Secondary School Mathematics Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 33-38). Reston, VA: National Council of Teachers of Mathematics. (posted on Blackboard)

Oct. 3, 2013

Henningsen, M. & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549. (posted on Blackboard)

Driscoll, M. (1999) Fostering Algebraic Thinking (Ch. 1). Portsmouth, NH: Heinemann (will be handed out in class)

Driscoll, M. (2010). Learning and Teaching Algebra in Secondary School Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 13-20). Reston, VA: National Council of Teachers of Mathematics. (will be handed out in class)

IMP mathematics unit for review (will be handed out in class)

4


Article(s)

Oct. 10, 2013

Geometry activities (will be handed out in class)

Driscoll, M. (2007). Fostering Geometric Thinking (Ch. 1). (will be handed out in class)

Oct. 17, 2013

Driscoll, M. (2010). Geometry and Proof in Secondary School Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 21-26). Reston, VA: National Council of Teachers of Mathematics. (will be handed out in class)

Oct. 24, 2013

White, P., & Mitchelmore, M. (1996). Conceptual knowledge in introductory calculus. Journal for Research in Mathematics Education, 27(1), 79-95. (posted on Blackboard)

Texas Instruments Activities Exchange: Calculus activities (activity will be specified in class) http://education.ti.com/educationportal/sites/US/nonProductSingle/activitybook_calculus_activities.html

Oct. 31, 2013

Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239-528. (posted on Blackboard)

Gutierrez, R. (2007). Context matters: Equity, success, and the future of mathematics education. In Lamberg, T., & Wiest, L. (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the international group for the Psychology of Mathematics Education, Stateline, NV: University of Nevada, Reno. (posted on Blackboard)

Nov. 7, 2013

Moschkovich, J. (2007). Bilingual Mathematics Learners: How views of language, bilingual learners, and mathematical communication affect instruction. In Nasir, N.S., & Cobb, P. (Eds.), Improving Access to Mathematics, Teachers College, Columbia University, 146-158. (posted on Blackboard)

Nov. 14, 2013

Zbiek, R. M. (2010). The Influence of Technology on Secondary School Students’ Mathematics Learning. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 39-44). Reston, VA: National Council of Teachers of Mathematics. (will be handed out in class)

Geometer’s Sketchpad activity (posted on Blackboard)

TI- calculator activity (will be handed out in class)

Nov. 21, 2013

Tall, D. (1989). The nature of mathematical proof. Mathematics Teaching, 127, 28–32. (can be downloaded as a pdf from Google Scholar, warwick.ac.uk).

CME mathematics activity (will be handed out in class)

5


Article(s)

Nov. 28, 2013

(no readings)

Dec. 5, 2013

Cobb, P., McClain, K., Lamberg, T. d. S., & Dean, C. (2003). Situating teachers' instructional practices in the institutional setting of the school and district. Educational Researcher, 32(6), 13-24. (posted on Blackboard)

Standards:

You will also need to download the Massachusetts Common Core Standards for Mathematics. Please bring this document to each class after the first.

The Common Core Standards for Mathematics can be found at:

http://www.doe.mass.edu/candi/commoncore/

You can also order the text that contains the standards from the Massachusetts Department of Education. If you are a current teacher, your school may have already provided you with the booklet that contains the Common Core.

Technology:

You will need to purchase or borrow a TI83+/84+ graphing calculator for use throughout the course. It may also be useful to download a trial or purchase MathType (mathematics equation editor) for the computer.

Note: Additional resources (not required) are listed at the end of the syllabus

INTENDED LEARNING OUTCOMES

In working towards the course goals, you will:

1. Design mathematics lesson plans that engage students in your classroom

2. Create mathematics tasks that promote conceptual understanding as well as the use of mathematical practices described in the Common Core State Standards

3. Create a unit plan guided by essential questions and essential understandings

4. Understand how research on learning informs teaching practice

6

5. Make connections between content/practice standards in mathematics and the tasks, lessons, and units you design

6. Analyze your own beliefs about the nature of mathematics and the nature of school mathematical practice

7. Reconstruct school mathematics to allow for creative possibilities for your students

ASSESSMENT OF LEARNING OUTCOMES

RESPONSE TO THE LITERATURE (1)

One 4-6 double-spaced page paper summarizing and responding to a theoretical or empirical article on a relevant mathematics education topic from those discussed in class.

The article can be chosen from the list provided in the syllabus (not in the required reading list) or can be obtained from a peer-reviewed journal in mathematics education. If the article is not listed in the resource section below, it must be approved first by the instructor prior to writing the response paper.

Use 1-2 pages to summarize the article(s), discussing the problem, the purpose of the work, and key findings. Two to four additional pages should reflect your reaction to the literature. For example, you might explain why the work is particularly important, review strengths and weaknesses of the study, or focus on the implications of the article/study for your own teaching practice. As you respond to the articles you choose, be sure to use actual evidence from the article and to show that you are thinking critically about the issue at hand. Use APA standards in your papers. Your literature responses will be shared in class.

Portion of final grade: 5%

UNIT DESIGN

An instructional unit including 6 lessons, two of which are turned in individually (see below).

The unit will be framed by essential questions and essential understandings. After selecting a content area for which to write the unit, you will write a mathematics-based essential question that will help students make connections among the mathematical ideas contained within the class activities you design. You will be asked to specify the unit’s position in a particular mathematics course, map out the scope and sequence of the mathematics topics covered in your unit, as well as identify objectives, content, pre-assessments, opening activities, in-class activities, homework, and assessment in your lessons. Each element of the instructional unit will also be explicitly connected to the essential question and understandings you identify. Emphasis will be placed on communicating the relevance of the mathematics content to your students. The lessons as well as the unit you design should also specify their connection to the Common Core mathematics content and practice standards.

7

An outline of the unit will be handed prior to writing specific lesson plans. This will serve as a blueprint and will specify learning objectives for the entire unit that will frame the learning objectives for the two formal lesson plans to be handed in (see below).

A rubric for your unit design will be handed out in class.


LESSON PLANS (2)

Two lesson plans written using the template introduced and discussed in class.

You will choose a mathematics course for which to write specific lesson plans. Your lesson plans will specify objectives (both content and academic language), purpose, pre-assessments, opening activities, in-class activities, homework and assessment. In preparing these, you will be asked to think critically about the kinds of questions that students will ask and the ways in which you can support their concept development while teaching. Through our coursework, we will learn to write effective, clear, meaningful, and student-centered lesson plans.

The second lesson plan will include the use of technology for improving student understanding of a particular mathematics idea. Technology includes the use of a tool that enhances students’ learning experiences. For example, students may use graphing calculators to represent a function in different ways; Geometer’s Sketchpad or Geogebra to perform transformations on a geometric object; or the use of an Excel spreadsheet to keep track and analyze data from an experiment.

A lesson plan rubric will be handed out in class. The two lesson plans you develop can be part of the final unit plan you create. Also, one of the lesson plans can be used in your teaching event for the field experience portion of this course (see below).

Portion of final grade: 35% (15% first lesson plan without adjustment (see below); 20% second lesson plan with technology)

ADJUSTED LESSON PLAN

The first lesson plan adjusted for the needs of diverse learners.

You will further develop the first lesson plan you write for this course to include supplemental activities for differentiating instruction in your classroom. Differentiation might include changes for students with special needs, for English Language Learners, or for students who need additional challenge on the mathematics content of your lesson.


FIELD EXPERIENCE

For the course field experience, you will observe two lessons and teach one lesson in a school classroom. If you are already a teacher of record, you will observe two lessons taught by another mathematics teacher at your school. For your teaching experience, you will videotape one of your class lessons that we will analyze collectively in our class, with a particular focus specified before videotaping your class.

8

If you are not yet a teacher of record, you will be assigned a collaborating teacher in a nearby school. You will be asked to visit the school for two observations of this teacher, and will also teach one class on your own that you will also videotape.

Focus of Observation #1: Eliciting Common Core Mathematical Practices

Focus of Observation #2: Developing academic language

Teaching Event: Enacting a math lesson in the classroom (introduction to the Teacher Performance Assessment and evaluation standards)


MATHEMATICS EDUCATOR SPEAKING SERIES

As part of this course, you will attend three speaker series relevant to the content for this course. During the weeks when speakers are scheduled, our Thursday night class will be 1 hour - 1.5 hours long instead of the 2.5 hours scheduled for the course. The first speaker is scheduled for Monday, September 23, from 4-6 pm, in Pasteur 106. Attendance is required. You will write a short 1-page response to the session in which you will explore how the ideas presented are relevant to your own teaching. Guiding questions for this short reflection are listed below:

1. What problem(s) does the speaker present in his/her session?

2. How does the work of the speaker address the mathematics education issue in focus?

3. So what? What can you take from the speaker’s presentation that can improve your own practice?

Speaker Dates: Monday, September 23, 4-6 pm; Monday, October 21, 4-6 pm; Monday, November 18, 4-6 pm


PARTICIPATION & ENGAGEMENT IN CLASS

You are expected to come prepared to class and to engage in class discussions. Coming prepared means that you have completed the readings and any other assignments due, and that you are ready to share your insights, ideas, and/or questions with the rest of the class. See below for the attendance and lateness policies, both of which can have an impact on your participation grade.


COURSE POLICIES

Attendance

You are expected to attend all of the class sessions and to participate fully in class. In the event that you must miss a class or part of a class, please let me know in advance so that we can set up a plan for making up work missed. If you have poor attendance or are consistently late to class,

9

the assessment of your contribution to the class will be affected (points deducted from the overall participation grade).

I expect you to attend each class, be punctual, and engage meaningfully in our class activities. Up to 5 points from your final grade may be deducted if you do not uphold your commitment to the course.

Late Work

All assignments must be submitted on time. If you believe you will need to turn in an assignment after it is due, please be sure to let the instructor know in advance. Points may be deducted from the overall grade of the assignment for lateness.

GRADES

Specific rubrics will be provided for the assignments outlined above. However, the overall grading system for the course is specified below. Note that the UMass system uses the range from B to A+ for graduate standard work.

General grading criteria

A + Work of the highest professional standard demonstrating independent and exemplary performance (99-100)

A Excellent work demonstrating independent and high quality performance (96-98)

A- Very good work, indicating consistent and careful thought and attention to the task, but requiring some areas of improvement (91-95)

B+ Good work, carefully executed, yet requiring several areas of improvement (86-90)

B Work of graduate standard, but omissions exist or careful analysis and/or consistency are not in evidence (80-85)

B- Effort is evident, but work indicates lack of understanding of the demands of the task. (76-79)

C+ Poor quality work with little attention to details and the demands of the task. (70-75)

C Work of very poor quality, indicating no understanding of the depth of analysis required (65-69)

10

F Serious neglect or evidence of cheating (65 or below)

IMPORTANT DUE DATES

Literature Response Paper: September 19

Instructional Unit Overview/Outline: October 3

Lesson plan #1: October 17

Adjusted lesson plan: November 7

Lesson Plan #2 (with technology): November 28

Instructional Unit: TBA (during reading period)

11

COURSE SEQUENCE

The following is a tentative topic sequence for the course (subject to change):

DATE

TOPIC

READINGS (TO BE COMPLETED IN ADVANCE OF THE CLASS DATE)

ASSIGNMENT (DUE ON THE CLASS

DATE)

Sept. 5

Introduction and course overview

The task of teaching mathematics

The nature of mathematics

Overview of the Common Core mathematics standards, with a focus on the practice standards

Sept. 12

Developing mathematical understanding and mathematical connections

Mathematical thinking and mathematical communities of practice

Continued analysis of standards for school mathematics

Preparing a literature response

Common Core standards

Ball, D., Thames, M. & Phelps, G. (2008)

12

DATE

TOPIC



DATE)

Sept. 19

Mathematics curriculum models: understanding the need for reform

Lesson Planning: Essential questions, content and academic language objectives, backwards design; connections to national standards

Literature response presentations

Giné, R., & Kruse, D. (2007).

Wiggins & McTighe: Understanding by Design

Boaler (1999)

Literature Response paper

*Sept 23: First Speaker

Sept. 26

(Shortened class)

Assessing mathematics learning

Mathematics curriculum models

Designing mathematical tasks: cognitive demand

Lesson Planning: Essential questions, content and academic language objectives, backwards design; connections to national standards

Literature response presentations

Smith and Stein (2010)

CME mathematics unit

Cuoco et al, Mathematical habits of mind (1996)

Speaker response

Oct. 3

Enactment of mathematics lessons: purposeful questioning and maintaining cognitive demand

Teaching algebraic thinking; algebraic habits of mind

Task focus: Algebra

Henningsen & Stein (1997)

Driscoll et al, Fostering Algebraic Thinking

Driscoll (2010)

Unit Outline

Teaching geometric thinking: geometric habits of mind Driscoll et al, Fostering Geometric Thinking (geometric habits of

13

DATE

TOPIC



DATE)

Oct. 10

Task focus: Geometry

mind) (2007)

Additional geometry activities

October 17

Teaching geometric thinking: geometric habits of mind

Task focus: Geometry

Driscoll (2010)

Lesson Plan #1

*Oct 21: Second Speaker

Oct. 24

(shortened class)

Teaching and learning precalculus & calculus

Task focus: Calculus

White & Mitchelmore, 1996

Texas Instruments Activities Exchange: Calculus activities

Speaker Response

Oct. 31

Equity and diversity in mathematics education

Unit design

Boaler (2002)

Gutierrez, R. (2007)

Nov. 7

Equity and diversity in mathematics education (English Language Learners)

Unit design (cont.)

Moschkovich, J. (2007) Lesson Plan #1,

adjusted for diverse learners

Nov. 14

Using technology in the mathematics classroom

Zbiek, R. M. (2010)

Geometer’s Sketchpad activity

14

DATE

TOPIC



DATE)

TI- calculator activity

*Nov. 18: Third

Speaker

Nov. 21

(shortened class)

Teaching and understanding proof

Tall, D. (1989)

CME Mathematics Activity

Speaker Response

Nov. 28

Analyzing student work

Instructional Unit workshop

No readings this week Lesson Plan #2 (with technology; no presentation)

Dec. 5

Professional and community engagement

Cobb, P. et al (2003)

Instructional Unit

(Due during Reading Period, TBA)

15

ADDITIONAL RESOURCES (NOT REQUIRED)

Below are different types of resources that may be useful to you, either for the purposes of this course, or for your future work with secondary mathematics students. The first list includes mathematics education research articles that you may use for your literature reviews. The research articles are of two types:

The second lists curriculum resources, including useful books, articles, and manuals for the integration of technology in your mathematics classroom.

Mathematics education research:

1. Ball, D., & Cohen, D. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-8, 14.

2. Beaton, A.E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., y Smith, T.A. (1998). Mathematics Achievement in the Final Year of Secondary School: IEA's Third

International Mathematics and Science Study (TIMSS).

3. Boaler, J. (2002). The development of disciplinary relationships: knowledge, practice, and identity in mathematics classrooms. For the Learning of Mathematics, 22(1), 42-47.

4. Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32-42.

5. Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121-143.

6. Bussi, M. B. (1998). Joint activity in mathematics classrooms: A Vygotskian analysis. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The Culture of the Mathematics Classroom (pp. 13-49). Cambridge: Cambridge University Press.

7. Cobb, P., & McClain, K. (1998). The role of imagery and discourse in supporting students’ mathematical development. In M. B. Lampert, & L. Merrie (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 56-82). New York, NY: Cambridge University Press.

8. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1&2), 113-163.

9. Cobb, P. (2006). Mathematics learning as a social process. In J. M. W. Schloeglmann (Ed.), New mathematics education and practice (pp. 147-152). Rotterdam: Sense Publishers.

10. Driscoll, M. (2007). Fostering Geometric Thinking: A Guide for Teachers, Grades 5-10. Newton, MA: Education Development Center.

16

11. Driscoll, M. (2010). Learning and Teaching Algebra in Secondary School Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 13-20). Reston, VA: National Council of Teachers of Mathematics.

12. Driscoll, M. (2010). Geometry and Proof in Secondary School Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 21-26). Reston, VA: National Council of Teachers of Mathematics.

13. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123): Kluwer Academic Publishers.

14. Giné, R., & Kruse, D. (2007). What if less is just less? The Role of depth over breadth in the secondary mathematics curriculum. Horace, 23(2), 5-15.

15. Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49, 193-223.

16. Gray, E., & Tall, D. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. Proceedings of PME25, 65-72.

17. Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37-73.

18. Gutstein, E., Lipman, P., Hernandez, P., & de los Reyes, R. (1997). Culturally relevant mathematics teaching in a Mexican American context. Journal for Research in Mathematics Education, 28(6), 709-737.

19. Ma, X. (2000). A longitudinal assessment of antecedent course work in mathematics and subsequent mathematical attainment. The Journal of Educational Research, 94(1), 16-28.

20. Ma, X., & Xu, J. (2004). Determining the causal ordering between attitude and achievement toward mathematics and achievement in mathematics. American Journal of Education, 110, 256-280.

21. Martin, D. B. (2007). Mathematics learning and participation in the African American context: The co-construction of identity in two intersecting realms of experience. In Nasir, N.S., & Cobb, P. (Eds.), Improving Access to Mathematics, Teachers College, Columbia University, 146-158.

22. Moody, V. (2001). The social constructs of the mathematical experiences of African-American students. In B. F. Atweh, & B. Nebres (Eds.), Sociocultural Research on Mathematics Education (pp. 255-276). Mahwah: Lawrence Erlbaum Associates, Inc.

23. Moschkovich, J. (2010). Language, Culture, and Equity in Secondary School Mathematics Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics:

17

Translating Research for Secondary School Teachers (pp. 75-79). Reston, VA: National Council of Teachers of Mathematics.

24. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

25. National Research Council. (2000). Everybody counts: A report to the nation on the future of mathematics education. Washington, D.C.: National Academies Press.

26. Oakes, J. (1990). Multiplying inequalities: The effects of race, social class, and tracking on opportunities to learn mathematics and science. Santa Monica, CA: The RAND Corporation.

27. Petersen, M., Kraus, B., & Windham, T. (2005). Striving toward equity: Underrepresented minorities and mathematics. SIAM News, 38(3).

28. Pirie, S.E.B., & Kieren, T. E. (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in

Mathematics, 26 (3), 165-190.

29. Remillard, J., Stein, M. K., Smith, M. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics. Charlotte, N.C.: Information Age Publishing.

30. Reys, R. E. (2001). Curricular Controversies in the Math Wars: A Battle Without Winners. Phi Delta Kappan, 83(3), 255-258.

31. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New York: MacMillan.

32. Schreiber, J. (2002). Institutional and student Factors and their influence on advanced mathematics achievement. The Journal of Educational Research, 95(5), 274-286.

33. Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46, 13-57.

34. Sfard, A. (2006). Participationist discourse on mathematics learning. In W. Schloeglmann (Ed.), New Mathematics Education Research and Practice (pp. 153-170). Rotterdam: Sense Publishers.

35. Smith, M. & M.K. Stein (2010). The Role of Curricular Materials in Secondary School Mathematics Classrooms. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 33-38). Reston, VA: National Council of Teachers of Mathematics.

18

36. Stanic, G. (1991). Social inequality, cultural discontinuity, and equity in school mathematics. Peabody Journal of Education, 66, 57-71.

37. Stein, M.K., & Henningsen. M. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549.

38. Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36, 157-195.

39. Tall, D. (1993). Students’ Difficulties in Calculus. Paper presented at the Working Group 3, ICME, Quebec.

40. Taylor, J. (2005). Achieving excellence in urban schools: Pitfalls, pratfalls, and evolving opportunities. The Negro Educational Review, 56(4).

41. Thompson, T., & Lewis, B. (2005). Shooting for the stars: A case study of the mathematics achievement and career attainment of an African American male high school student. The High School Journal, 6-18.

42. Highlights From TIMSS 2007: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context. (2007). Published by National Center for Education Statistics. Download from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001

43. Treisman, U. (1992). Studying students studying calculus: A look at the lives of minority mathematics students in college. The College Mathematics Journal, 23(5), 362-372.

44. Zbiek, R. M. (2010). The Influence of Technology on Secondary School Students’ Mathematics Learning. In J. Lobato & F. Lester (Eds.), Teaching and Learning Mathematics: Translating Research for Secondary School Teachers (pp. 39-44). Reston, VA: National Council of Teachers of Mathematics.

Mathematics curriculum & pedagogy:

1. Artzt, A. F., & Newman, C. M. (1997). How to use cooperative learning in the mathematics class. Reston, VA: NCTM.

2. Berlinski, D. (1995). A Tour of the calculus. New York: Random House.

3. Johnson, D. R. (1982). Every minute counts: Making your math class work. Palo Alto: Dale Seymour Publications.

4. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.

5. Steen, L. A. (Ed.). (1990). On the shoulders of giants. Washington, DC: National Academy Press.

19

6. Tomlinson, C.A. (1999). The Differentiated classroom: Responding to the needs of all learners. ASCD.

7. SIMMS Integrated Mathematics: http://www.montana.edu/wwwsimms/

8. Consortium for Mathematics and its Applications: http://www.comap.com/

9. Core-Plus Mathematics Project: http://www.wmich.edu/cpmp/index.html

Suggested websites:

National Council of Teachers of Mathematics: http://www.nctm.org

Illuminations at NCTM: http://www.illuminations.nctm.org

Texas Instruments: http://education.ti.com

The Math Forum: http://mathforum.org

Association for Supervision and Curriculum Development: http://www.ascd.org

Teacher Professional Development by Annenberg: http://www.learner.org/resources/browse.html

PBS for teachers: http://www.pbs.org/teachers/mathline/concepts/moremathconcepts.shtm

Archives of mathematics topics and activities: http://archives.math.utk.edu/topics/

Hands-on mathematics units: http://www9.georgetown.edu/faculty/sandefur/handsonmath/download.htm

Problems with a Point: http://www2.edc.org/mathproblems/

Geometer’s Sketchpad Resources: http://www.dynamicgeometry.com/General_Resources/Classroom_Activities.html

Geometer’s Sketchpad Sample Activities: http://learningcenter.dynamicgeometry.com/x20.xml

Interactive Math Program sampler: http://www.mathimp.org/curriculum/samples.html

Core-Plus sample materials: http://www.wmich.edu/cpmp/programoverview.html

CME (Center for Mathematics Education at Education Development Center) project: http://cmeproject.edc.org/

CURRICULUM AND TEACHING-- SECONDARY MATHEMATICS … Curriculum and Teaching Math_tcm1… · ( ......

Documents

Transcript of CURRICULUM AND TEACHING-- SECONDARY MATHEMATICS … Curriculum and Teaching Math_tcm1… · ( ......