Elementary Methods and Content

Video Resources for Instructors

  • Annenberg Media’s K-4 Video Library highlighting how the NCTM Standards are reflected in elementary classrooms. http://www.learner.org/resources/series32.html
  • Carpenter, T., Franke, M. L., & Levi, L. (2003).  Thinking mathematically: Integrating arithmetic and algebra in elementary school.  Portsmouth, NH: Heinemann.
  • Carpenter and colleagues are working on a second edition of CGI, which is said to include updated video clips
  • Catherine Fosnot and colleagues’ video resources around Young Mathematicians At Work (facilitator’s packages include overview manual, facilitators guide, and interactive CD). http://www.heinemann.com/authors/productsByAuthor.aspx?id=293
  • Parrish, S. (2010).  Number Talks: Helping children build mental math and computation strategies (A multimedia professional learning resources) . Sausalito, CA: Math Solutions.
  • Philipp, R. & Schappelle, B. (2012).  Integrating Mathematics and Pedagogy (IMAP): Searchable collection of children’s-mathematical-thinking video clips.  Boston, MA: Pearson.
  • Storeygard, J. (2009).  My kids can: Making math accessible to all learners, K-5.  Portsmouth, NH: Heinemann.

Research on Children’s Mathematical Thinking

  • Carpenter, T. (1985). Learning to add and subtract: An exercise in problem solving. In E. Silver (Ed.),  Teaching and learning mathematical problem solving: Multiple research perspectives  (pp. 17-40).  Hillsdale, NJ: Erlbaum.
  • Carpenter, T., Fennema, E., Peterson, P. & Carey, D. (1988). Teachers’ pedagogical content knowledge of students’ problem solving in elementary arithmetic.  Journal for Research in Mathematics Education ,  19 , 385-401.
  • Carpenter, T., Fennema, E., Peterson, P., Chiang, C., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study.  American Educational Research Journal ,  26  (4), 499-531.
  • Carpenter, T., Franke, M. L., & Levi, L. (2003).  Thinking mathematically: Integrating arithmetic and algebra in elementary school.  Portsmouth, NH: Heinemann.
  • Chamberlin, M. (2005). Teachers' discussions of students' thinking: Meeting the challenge of attending to students' thinking.  Journal of Mathematics Teacher Education, 8 , 141-170.
  • Empson, S. B., Junk, D., Dominguez, H., & Turner, E.  (2006) Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking. Educational Studies in Mathematics,  63, 1, 1-28.
  • Empson, S. B., & Levi, L. (2011).  Extending children’s mathematics fractions and decimals: Innovations in Cognitive Guided Instruction.  Portsmouth, NH: Heinemann.
  • Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (Fall, 1993).  Using children's knowledge in instruction.  American Educational Research Journal, 30  (3), 555-583.
  • Fuson, K. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning  (pp. 243-275). New York: Macmillan.
  • Jacobs, V., Ambrose, R., Clement, L. & Brown, D. (2006). Using teacher produced videotapes of student interviews as discussion catalysts.  Teaching Children Mathematics , 276-281.
  • Kazemi, E., & Franke, M. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry . Journal of Mathematics Teacher Education , 7(3), 203–235.
  • Villasenor, A., & Kepner, H., "Arithmetic from a Problem-Solving Perspective: An Urban Implementation,"  Journal for Research in Mathematics Education,  24 (1), 1993, pp. 62- 69.

Research on Diversity, Equity and Children’s Funds of Knowledge Related to Mathematics

  • Brenner, M. (1998). Development of mathematical communication in problem solving groups by language minority students.  Bilingual Research Journal , 22, 2, 3 & 4, 149-175.
  • Cahnmann, M. & Remillard, J. (2002). What counts and how: Mathematics teaching in culturally, linguistically, and socioeconomically diverse urban settings.  The Urban Review, 34  (3), 179-204.
  • Civil, M. (2006). Building on community knowledge: An avenue to equity in mathematics education. In N. Nasir and P. Cobb (Eds.),  Improving access to mathematics: Diversity and equity in the classroom  (pp. 105-117) .  New York: Teachers College Press.
  • Civil, M. (2002). Culture and Mathematics: A community approach.  Journal of Intercultural Studies , 23 (2), 133-148.
  • de Abreu, G. (1995). Understanding how children experience the relationship between home and school mathematics.  Mind, Culture, and Activity , 2(2), 119–142.
  • Ensign, J. (2005). Helping teachers use students’ home cultures in mathematics lessons: Developmental stages of becoming effective teachers of diverse students. In A. Rodriguez & R. Kitchen (Eds.),  Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy  (pp. 225-242). Mahwah, NJ: Lawrence Erlbaum.
  • Geary, D. (2004). Mathematics and learning disabilities.  Journal of Learning Disabilities, 37  (10), 4-15.
  • González, N., Moll, L. & Amanti, C. (2005).  Funds of knowledge: Theorizing practices in households, communities, and classrooms.   Mahwah, NJ: Lawrence Earlbaum.
  • González, N., Andrade, R., Civil, M., Moll, L. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics.  Journal of Education for Students Placed at Risk , 6 (1&2), 115-132.
  • Gutiérrez, R. (2002). Beyond Essentialism: The Complexity of Language in Teaching Mathematics to Latina/o Students.  American Educational Research Journal, 39 (4), 1047- 1088.
  • Gutsetin, E., Lipman, P., Hernandez, P., & Reyes, R. (1997). Culturally relevant mathematics teaching in a Mexican American context.  Journal for Research in Mathematics Education , 28 (6), 709-737.
  • Karp, K. (2004). Building responsibility for learning in students with special needs.  Teaching Children Mathematics, 11 (3), 118-126.
  • Khisty, L. (1995). Making inequality: issues of language and meaning in mathematics teaching with Hispanic students. In W. Secada, E. Fennema, & L. Adajain (Eds.),  New directions for equity in mathematics education  (pp. 279-297). New York: Cambridge.
  • Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy.  American Education Research Journal , 32 (3), 465-491.
  • Lipka, J. (2005). Math in a cultural context: Two case studies of a successful culturally based math project. Anthropology and Education Quarterly , 36(4), 367–385.
  • Lubienski, S. T. (2007).  Research, reform and equity in mathematics education. In N. S. Nasir & P. Cobb [Eds.]  Improving access to mathematics: Diversity and equity in the classroom (pp. 10-23). New York: Teacher’s College Press.
  • Lubienski, S. T. (2000).  Problem solving as a means toward "mathematics for all":  An exploratory look through a class lens.   Journal for Research in Mathematics Education , 31 (4), 454-482.
  • Maldonado, L., Turner, E., Dominguez, H. & Empson, S.  (2008, in press). English Language Learners Learning From and Contributing To Mathematical Discussion .  To appear in Mathematics for ALL: Instructional Strategies for Diverse Classrooms: Grades 3- 5 .  Reston, VA: NCTM.
  • Matthews, L. (2003). Babies overboard! The complexities of incorporating culturally relevant teaching into mathematics instruction.  Educational Studies in Mathematics,  53, 61-82.
  • Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms.  Theory into Practice , 31 (2), 132-141.
  • Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners.  Mathematical Thinking and Learning, 4  (2&3), 289-212.
  • Nasir, N., Hand, V. & Taylor, E. (2008). Culture and Mathematics in School: Boundaries Between "Cultural" and "Domain" Knowledge in the Mathematics Classroom and Beyond.  Review of Research in Education , 32(1): 187 - 240.
  • Tate, W. (1994, February). Race, retrenchment and the reform of school mathematics.  Phi Delta Kappan , 477-484.
  • Wager, A. A., & Whyte, K. (2013). Young children’s mathematics: Whose home practices are privileged?  Journal of Urban Mathematics Education, 6 (1), 81-95.
  • Wager, A. A. (2012). Incorporating out-of-school mathematics: From cultural context to embedded practice.  Journal of Mathematics Teacher Education, 15 (1), 9 – 23.

Research on Integrating Children’s Mathematical Thinking with Children’s Funds of Knowledge

  • Aguirre, J., Turner, E. E., Bartell, T., Craig, C. K., Foote, M. Q., Roth McDuffie, A., Drake, C. (2013). Making connections in practice: How prospective elementary teachers connect to children’s mathematical thinking and community funds of knowledge in mathematics instruction.   Journal of Teacher Education 64 (2), 178-192.
  • Foote, M. (2006). Joining a study of culture and mathematical thinking by examining an individual child. In Alatorre, S., Cortina, J.L., Sáiz, M., and Méndez, A.(Eds) Proceedings of the 28 annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 693 . Mérida, México: Universidad Pedagógica Nacional.
  • Foote, M. Q. (2009). Stepping out of the classroom: Building teacher knowledge for developing classroom practice. Teacher Education Quarterly , 36(3), 39-53.
  • Rodriguez, A. (2005). Using sociotransformative constructivism to respond to teachers’ resistance to ideological and pedagogical change. In A. Rodriguez & R. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy  (pp. 17-32). Mahwah, NJ:Lawrence Erlbaum.
  • Turner, E., Celedon-Pattichis, S., & Marshall, M. A. (2008).  Opportunities to LearnProblem Solving and Mathematics Discourse among Latino/a Kindergarten Students. In R. Kitchen & E. Silver (Eds.) Promoting high participation and success in mathematics by Hispanic students: Examining opportunities and probing promising practices [A Research Monograph of TODOS: Mathematics for ALL] Washington D.C.: National Education Association Press.

Readings related to Community Mathematics Explorations

  • Buck, P. & Skilton-Sylvester, P. (2005). Pre-service teachers enter urban communities: Coupling fund of knowledge research and critical pedagogy in teacher education. In González, N., Moll, L. & Amanti, C. (Eds.), Funds of knowledge: Theorizing practices in households, communities, and classrooms.   (p.213-232). Mahwah, NJ: Lawrence Earlbaum.
  • Civil, M. (2006). Building on community knowledge: An avenue to equity in mathematics education. In N. Nasir and P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 105-117) . New York: Teachers College Press.
  • Civil, M. (2002). Culture and Mathematics: A community approach. Journal of Intercultural Studies , 23 (2), 133-148.
  • de Abreu, G. (1995). Understanding how children experience the relationship between home and school mathematics. Mind, Culture, and Activity , 2(2), 119–142.
  • Drake, C. & Norton-Meier, L. (2007). Creating Third Spaces: Integrating Family and Community Resources into Elementary Mathematics Methods. Paper presented at the annual meeting of PME-NA, October 25, 2007.
  • Ensign, J. (2005). Helping teachers use students’ home cultures in mathematics lessons: Developmental stages of becoming effective teachers of diverse students. In A. Rodriguez & R. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 225 - 242). Mahwah, NJ: Lawrence Erlbaum.
  • González, N., Moll, L. & Amanti, C. (2005). Funds of knowledge: Theorizing practices in households, communities, and classrooms.   Mahwah, NJ: Lawrence Earlbaum.
  • Ladson-Billings, G.J. (1999). Preparing Teachers for Diverse Student Populations: A Critical Race Theory Perspective.Review of Research in Education , 24, 211-247.
  • Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Education Research Journal , 32 (3), 465-491.
  • Lipka, J. (2005). Math in a cultural context: Two case studies of a successful culturally based math project.Anthropology and Education Quarterly , 36(4), 367–385.
  • Milner, H. R. & Smithney, M. (2003). How teacher educators created a course curriculum to challenge and enhance preservice teachers’ thinking and experience with diversity. Teaching Education, 14 (3), 293-305.
  • Civil, M. & Kahn, L. H. (2001). Mathematics instruction developed from a garden theme. Teaching Children Mathematics,  7 (7), 400-405.
  • Flores, A. (1997). Sí se puede. It can be done: Quality mathematics in more than one language. In J. Tentracosta (Ed.), Multicultural and gender equity in the mathematics classroom (p. 81-91). Reston, VA: National Council of Teachers of Mathematics.
  • González, N., Andrade, R., & Carson, C. (2001). Creating links between home and school mathematics practices. In E. McIntyre, A. Rosebery, & N. Gonzalez (Eds.), Classroom diversity: Connecting curriculum to students’ lives (pp. 100–114). Portsmouth, NH: Heinemann.
  • Gutstein E. & Peterson, B. (2005). Rethinking Mathematics: Teaching Social Justice by the Numbers (pp. 117-120). Milwaukee: Rethinking Schools Publications.
  • Kahn, L. & Civil, M. (2001). Unearthing the mathematics of a classroom garden. In E. McIntyre, A. Rosebery, & N. González (Eds.), Classroom diversity: Connecting school to students’ lives (pp. 37 - 50). Portsmouth, NH: Heinemann.
  • Kyle, D., McIntyre, E., & Moore, G. (2001). Connecting mathematics instruction with the families of young children.Teaching Children Mathematics , 80-86.
  • Lo Cicero, A., Fuson, K., & Allexsaht-Snider, M. (2001), Mathematizing children's stories, helping children solve word problems, and supporting parental involvement . In W. Secada (Ed.) Changing the Faces of Mathematics: Perspectives on Latinos (pp. 59-70). Reston, VA: NCTM.
  • Torres-Velásquez, D. (2004). Culturally responsive mathematics teaching and English Language Learners. Teaching Children Mathematics , 249-255.
  • Turner, E. & Font Strawhun, B. (2007, May). Posing problems that matter: Investigating school overcrowding.Teaching Children Mathematics . (pp. 457-463).
  • Turner, E. & Font Strawhun, B. (2005). With Math, It's Like You Have More Defense. In Gutstein E. & Peterson, B. (Eds.), Rethinking Mathematics: Teaching Social Justice by the Numbers , (pp. 81-87). Milwaukee: Rethinking Schools Publications.

Mathematics Tasks

  • Breyfogle, M. L. & Williams, L. E. (2008/2009). Designing and implementing worthwhile tasks. Teaching Children Mathematics, 276 – 280.
  • Caufield, R., Harkness, S. S. & Riley, R. (2003). Surprise! Turning routine problems into worthwhile tasks. Mathematics Teaching in the Middle School, 198 – 201.
  • Cirillo, M., Herbel-Eisenmann, B. & Drake, C. (2009). Using curriculum to focus on understanding. Mathematics Teaching in the Middle School, 15 (1), 51 – 56.
  • Felton, M. D. (2010). Is math politically neutral? Teaching Children Mathematics, 60 – 63.
  • Kabiri, M. S. & Smith, N. L. (2003). Turning traditional textbook problems into open-ended problems. Mathematics Teaching in the Middle School, 186 – 192.
  • Land, T., Drake, C., Bartell, T.G., Aguirre, J., Foote, M.Q., Roth McDuffie, A., & Turner, E. E. (in press). Three strategies for opening curriculum spaces. Teaching Children Mathematics.
  • Peressini, D. & Knuth, E. (2000). The role of tasks in developing communities of mathematical inquiry. Teaching Children Mathematics, 391 – 397.
  • Smith, M. S., Bill, V. & Hughes, E. K. (2008). Thinking through a lesson: successfully implementing high-level tasks.Mathematics Teaching in the Middle School, 14 (3), 132 – 138.
  • Stallings, L. L. (2007). See a different mathematics. Mathematics Teaching in the Middle School, 13 (4), 212 – 217.

Classroom Discourse/Norms for Discussion

 

  • Chapin, S. H., O’Connor, C., & Anderson, N. C. (2009). Classroom discussions: using math talk to help students learn (2nd Edition). Sausalito, CA: Scholastic, Inc.
  • Chapin, S. H., & O'Connor, C. (2007). Academically productive talk: Supporting students' learning in mathematics. In W. G. Martin & M. E. Strutchens (Eds.), The learning of mathematics (pp. 113-128). Reston, VA: The National Council of Teachers of Mathematics.
  • Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79 (2), 1008-1043.
  • Herbel-Eisenmann, B., & Cirillo, M. (Eds.). (2009). Promoting purposeful discourse . Reston, VA: NCTM.
  • Jacobs, V. R. & Ambrose, R. C. (2008/2009). Making the most of story problems. Teaching Children Mathematics , 260 – 266.
  • Maldano, L. A., Turner, E. E., Dominguez, H., & Empson, S. B. (2009). English-language learners learning from, and contributing to, mathematical discussions. In D. White & J. Spitzer (Eds.) Mathematics for Every Student: Responding to Diversity, Grades PreK-5 (pp. 7 – 22). Reston, VA: National Council of Teachers of Mathematics.
  • Parks, A. N. (2009). Can teachers be too open? Teaching Children Mathematics, 424 – 428.
  • Roth McDuffie, A., & Young, T. A. (2003). Promoting mathematical discourse through children’s literature. Teaching Children Mathematics, 385 – 389.
  • Smith, M. S. & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
  • Staples, M., & Colonis, M. M. (2007). Making the most of mathematical discussions. Mathematics Teacher, 101 (4), 257-261.
  • Turner, E., Celedon-Pattichis, S., & Marshall, M. A. (2008). Opportunities to learn problem solving and mathematics discourse among Latino/a kindergarten students. In R. Kitchen & E. Silver (Eds.), Promoting high participation and success in mathematics by Hispanic students: Examining opportunities and probing promising practices [A Research Monograph of TODOS: Mathematics for ALL] Washington, D. C.: National Education Association Press.