A Selection of CGI Publications

Updated February 2019


Alexander, C. & Ambrose, R. (August 2010). Digesting student-authored story problems. Mathematics Teaching in the Middle School, 16, (1), 27-33.

Ambrose, R. (2004). Initiating Change in Prospective Elementary School Teachers’ Orientation to Mathematics Teaching by Building on Beliefs.  Journal of Mathematics Teacher Education 7(2), 91-119 

Ambrose, R., Baek, J., Carpenter, T. P., (2003). Children’s Invention of Multiplication and Division Algorithms, in Baroody, A. and Dowker (Eds.) The Development of Arithmetic Concepts and Skills: Recent Research and Theory.Mahwah, NJ: Erlbaum. 

Ambrose, R. & Kenehan, G. (2009). Children's Evolving Understanding of Polyhedra in the Classroom, Mathematical Thinking and Learning, Vol 11 (3), 158 - 176.

Ambrose, R. & Molina, M. (in press). First-grade Latino English Language Learners´ performance on story problems in English versus Spanish. Canadian Journal of Science, Mathematics and Technology Education.

Baek, J. M. (2008). Developing algebraic thinking through explorations in multiplication. In C. Greenes (Ed.), Algebra and algebraic thinking in school mathematics: NCTM 2008 Yearbook. Reston, VA: National Council of Teachers of Mathematics.

Baek, J. M. (2005). Children’s mathematical understanding and invented strategies for multidigit multiplication. Teaching Children Mathematics, 12, 242-247.

Baek, J. (1998). Children’s invented algorithms for multidigit multiplication problems. In Morrow, L. (Ed). The teaching and learning of algorithms in school mathematicsReston, VA: National Council of Teachers of Mathematics.

Baek, J. M. & Flores, A. (2005). How does it feel? Teachers count on the alphabet, instead of numbers. Teaching Children Mathematics, 12, 54-59.

Battey, D. & Chan, A. (2010). Building community and relationships that support critical conversations on race: The case of Cognitively Guided Instruction. In M. Q. Foote (Ed.), Mathematics Teaching & Learning in K-12: Equity and Professional Development. New York: Palgrave.

Battey, D. & Franke, M. L. (2008). Transforming identities: Understanding teachers across professional development and classroom practice. Teacher Education Quarterly35(3), 127-149.  

Battey, D. & Franke, M. (2015). Integrating professional development on mathematics and equity: Countering deficit views of students of color. Education and Urban Society, 47(4), 433-462, first published on August 29, 2013 doi:10.1177/0013124513497788.

Battey, D. & Stark, M. (2009). Equitable classroom practices: Avoiding ability attributions from misconceptions in mathematics.  In C. Malloy (Ed.),Mathematics for All: Instructional Strategies for Diverse Classrooms (pp. 167-177). Reston, VA: National Council of Teachers of Mathematics.

Battey, D. & Neal, R. A. (2018). Detailing relational interactions in urban elementary mathematics classrooms. Mathematics Teacher Education and Development, 20(1), 23-42.

Battey, D., Neal, R., Leyva, L., & Adams-Wiggins, K. (2016). The interconnectedness of relational and content dimensions of quality instruction: Supportive teacher–student relationships in urban elementary mathematics classrooms. Journal of Mathematical Behavior, 42, 1-19.

Behrend, J. L. (2003). Learning-Disabled students make sense of mathematics. Teaching Children Mathematics, 9(1), 269-273.

Behrend, J. L. (2001). Are rules interfering with children’s mathematical understanding? Teaching Children Mathematics, 8(1), 36-40.

Behrend, J. L. & Mohs, L. C. (2005/2006). From simple questions to powerful connections: A two-year conversation about negative numbers. Teaching Children Mathematics, 12(5), 260-268.

Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2016). Leveraging structure: Logical necessity in the context of integer arithmetic. Mathematical Thinking and Learning18(3), 209–232.

Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2016). Unlocking the structure of positive and negative numbers. Mathematics Teaching in the Middle School22(2), 84–91.

Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., Schappelle, B. P., & Lewis, M. L. (2014). Obstacles and affordances for integer reasoning: An analysis of children’s thinking and the history of mathematics. Journal for Research in Mathematics Education45(1), 19–61.

Bishop, J. P., Lamb, L. L., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2014). Using order to reason about negative numbers: The case of Violet. Educational Studies in Mathematics86, 39–59.

Bishop, J. P., Lamb, L. L., Philipp, R. A., Schappelle, B. P., & Whitacre, I. (2011). First graders outwit a famous mathematician. Teaching Children Mathematics17, 350–358.

Bray, W.S., & Blais, T. V. (2017). Stimulating base-ten reasoning with context. Teaching Children Mathematics, 24(2), 120-127.

Bray, W. S., & Maldonado, L. A. (2018). Foster fact fluency with number string discussions. Teaching Children Mathematics, 25(2), 86–93.

Brickwedde, J. (2018). Place value as a rate of ten. Teaching Children Mathematics, 25 (1), 30-35. 

Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E., & Weisbeck, L. (1993). Models of problem solving:  A study of kindergarten children's problem-solving processes.  Journal for Research in Mathematics Education, 24(5), 428-441.

Carpenter, T. P., Fennema, E., Franke, M. L. (1999). Cognitively Guided Instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20.

Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L, Empson, S. B. (2015). Children’s mathematics: Cognitively guided instruction, Second Edition Portsmouth, NH: Heinemann.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.P., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching:  An experimental study.  American Educational Research Journal, 26 (4), 385-531.

Carpenter, T.P., Franke, M. L., Jacobs, V. R., Fennema, E., and Empson, S. B. (1998). A longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3-20.

Carpenter, T.P., Franke. M.L., Johnson, N.C., Turrou, A.C., Wager, A. A. (2017). Young children’s mathematics: Cognitively Guided Instruction in Early Childhood Education.Portsmouth, NH: Heinemann.

Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic & algebra in elementary school. Portsmouth, NH: Heinemann.

Carpenter, T. P., Levi, L., Franke, M. L., Zeringue, J. K. (2005).  Algebra in the Elementary School: Developing Relational Thinking.  ZDM – The International Journal on Mathematics Education37(1)

Carpenter, T. P., and Moser, J. M. (1984). The Acquisition of Addition and Subtraction Concepts in Grades One through Three.  Journal for Research in Mathematics Eduaction, 15(3), 179-202.

Chan, A.G. (2010). Identity and practice: Preservice teacher learning within a practice-based mathematics methods course.  Unpublished doctoral dissertation, University of California, Los Angeles.

Empson, S. B. (2003). Low-Performing Students and Teaching Fractions for Understanding: An Interactional Analysis. Journal for Research in Mathematics Education34: 4  305-343.

Empson, S.B., (2001). Equal Sharing and the Roots of Fractions Equivalence. Teaching Children Mathematics7: 421-25.

Empson, S.B., (1999) Equal Sharing and Shared Meaning: The Development of Fraction Concepts in a First-Grade Classroom. Cognition and Instruction17: 283-342.

Empson, S. B. (1995).  Using sharing situations to help children learn fractions.  Teaching Children Mathematics, 2(2), 110-114.

Empson, S. B. & Jacobs, V. J. (2008). Learning to Listen to Children’s Mathematics. In T. Wood (Series Ed.) & P. Sullivan (Vol. Ed.), International handbook of mathematics teacher education, vol.1: Knowledge and beliefs in mathematics teaching and teaching development(pp. 257-281). Rotterdam, the Netherlands: Sense Publishers.

Empson, S. B., Junk, D., Dominguez, H., and Turner, E. (2006). Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking. Educational Studies in Mathematics.

Empson, S. B. & Knudsen, J. (2003). Building on Children’s Thinking to Develop Proportional Reasoning. Texas Mathematics Teacher, L(2), 16-21.

Empson, S. B., and Levi, L. (2011) Extending Children’s Mathematics: Fractions and Decimals.Portsmouth, NH: Heinemann.

Empson, S. B., Levi, L., and Carpenter, T. P. (2010) The algebraic nature of fractions: developing relational thinking in elementary school in J Cai and E. Knuth (Eds) Early Algebraization: Cognitive, Curricular and Instructional Perspectives.  New York: Springer

Enyedy, N., Wischnia, S. & Franke, M.  (2008).  Classroom discourse : Contrastive and Consensus conversations.  Journal of Educational Research,  (2) 2./3.

Falkner, K. P., Levi, L., & Carpenter, T.P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 232-236.

Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction.  Journal for Research in Mathematics Education. 27, 4, 403-434.

Fennema, E., Carpenter, T. P., Jacobs, V. R., Franke, M. L., & Levi, L. (1998). A longitudinal study of gender differences in young children’s mathematical thinking.  Educational Researcher, 27(5), 4 – 12.

Fennema, E., Carpenter, T.P, Levi, L., Franke, M.L. & Empson, S. B. (2000). Children’s Mathematics: Cognitively Guided InstructionA Guide for Workshop Leaders. Portsmouth, NH: Heinemann.

Foote & Lambert (2011). Mary Foote and I wrote a paper about students with IEPs engaging in a CGI algebra routine. 

Foote, M. Q., & Lambert, R. (2011). I have a solution to share: Learning through equitable participation in a mathematics classroom. Canadian Journal of Science, Mathematics and Technology Education11(3), 247–260. https://doi.org/10.1080/14926156.2011.595882

Franke, M.L. (2003). Fostering young children's mathematical understanding. In C. Howes (Ed.) Teaching 4- to 8-year olds: Literacy, math, multiculturalism, and classroom community.  Baltimore, MD: Brookes.

Franke, M. L., Carpenter, T. P., & Battey, D. (2007). Content matters: The case of algebraic reasoning in teacher professional development. In J. Kaput, D. Carraher, & M. Blanton, (Eds.)Algebra in the Early Grades (pp. 333-359). Hillside, NJ: Lawrence Erlbaum.

Franke, M. L., Carpenter, T., Fennema, E., Ansell, E., and Behrend, J. (1998). Understanding Teachers' Self-Sustaining, Generative Change in the Context of Professional Development. Teaching and Teacher Education14(1), 67-80.

Franke, M.F., Carpenter, T.P., Levi, L., Fennema, E. (2001) “Capturing Teachers’ Generative Change: A Follow-up Study of Professional Development in Mathematics. American Educational Research Journal38 (3), 653-689.

Franke, M. L. and Kazemi, E. (2001). Learning to Teach Mathematics: Focus on Student Thinking.  Theory Into Practice 40(2), 102-109.

Franke, M.L., & Kazemi, E. (2001).  Teaching as learning within a community of practice: Characterizing generative growth.  In T. Wood, B. Nelson, & J. Warfield (Eds.). Beyond classical pedagogy in elementary mathematics: The nature of facilitative teaching (pp. 47-74). Mahwah, NJ:  Erlbaum.

Franke, M. L., Kazemi, E., & Battey, D. (2007).  Understanding teaching and classroom practice in mathematics.  In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225-256).  Greenwich, CT: Information Age Publishers.

Franke, M., Kazemi, E., Shih, J., Biagetti, S., & Battey, D. (2005). Changing teachers’ professional work in mathematics: One school’s journey. In T.A. Romberg,T.P. Carpenter, T. P., & F. Dremock (Eds.) Understanding mathematics and science matters (pp. 209-230).Mahwah, NJ: Erlbaum. 

Franke, M. L., Kazemi, E., Turrou, A. C. (2018). Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom.Portland, ME: Stenhouse.

Franke, M., Webb, N., Chan, A., Battey D.,  Ing, M., Freund, D., De, T. (2009). Eliciting student thinking in elementary mathematics classrooms: Practices that support understanding.  Journal of Teacher Education. 

Franke, M. L., Webb, N. M., Chan, A., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 364-379.

Gadge, U. (2018). Effects of Cognitively Guided Instruction on teacher created opportunities to engage students in problem-solving. (Unpublished doctoral dissertation). University of Miami, Miami, FL.

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Oliver, A., and Human, P. (1997) A day in the life of one Cognitively Guided Instruction Classroom, in Hiebert, et. al., Making Sense: Teachers and learning mathematics with understanding. Portsmouth, NH: Heinemann.

Jacobs, V. R. & Ambrose, R. C. (2008).  Making the most of story problems.  Teaching Children Mathematics, 15, 260–266.

Jacobs, V. R., Ambrose, R. C., Clement, L., and Brown, D. (2006).  Using Teacher-Produced Videotapes of Student Interviews as Discussion Catalysts.  Teaching Children Mathematics 12(6), 276-295.

Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM–The International Journal on Mathematics Education, 48(1–2), 185–197.

Jacobs, V. R., Empson, S. B., Pynes, S., Hewitt, A., Jessup, N., & Krause, G. (in press). Responsive teaching in elementary mathematics (RTEM) project.  In P. Sztajn & P. H. Wilson (Eds.), Designing professional development for mathematics learning trajectories.  New York: Teachers College Press.

Jacobs, V. R., Martin, H., Ambrose, R. C., Philipp, R. A. (2014).  Warning signs for taking over children’s thinking.  Teaching Children Mathematics21, 107–113.

Iuhasz-Velez, N., (2018). Effects of Cognitively Guided Instruction professional development on teachers' ability to predict student success on mathematical tasks – toward a conceptual framework on teachers’ knowledge of their students(Doctoral dissertation).

Jacobs, V. R., Franke, M. L., Carpenter, T.P., Levi, L., & Battey, D. (2007) Professional Development Focused on Children’s Algebraic Reasoning in Elementary School.  Journal for Research in Mathematics Education, May 2007

Jacobs, V. R., & Kusiak, J. (2006).  Got tools?  Exploring children's use of mathematics tools during problem solving.  Teaching Children Mathematics12, 470–477.

Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010).  Professional noticing of children’s mathematical thinking.  Journal for Research in Mathematics Education41(2), 169–202. 

Jacobs, V. R., Lamb, L. L. C., Philipp, R. A., & Schappelle, B. P. (in press).  Deciding how to respond on the basis of children's understandings.  In M. G. Sherin, V. R., Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing:  Seeing through teachers' eyes.  New York: Routledge.

Jacobs, V. R., & Philipp, R. A. (2010). Supporting children's problem solving. Teaching Children Mathematics, 17(2), 98–105.

Jacobs, V. R., & Philipp, R. A., (2004). Mathematical Thinking: Helping Prospective and Practicing Teachers Focus.  Teaching Children Mathematics, 11(4), 194-201.

Jaslow, L. & Jacobs, V. (2009, Spring).  Helping kindergartners make sense of numbers to 100.  TheJournal of Mathematics and Science: Collaborative Explorations11, 195–213.

Kazemi, E. (2003). Classroom practices that support children’s mathematical ideas.  In C. Howes (Ed.) Teaching 4- to 8-year olds: Literacy, math, multiculturalism, and classroom community (pp. 113-134).  Baltimore, MD: Brookes.

Kazemi, E. (2002). Exploring test performance in mathematics: The questions children’s answers raise.  Journal of Mathematical Behavior, 21,203-224.  

Kazemi, E., & Franke, M. L. (2004). Teacher Learning in Mathematics:  Using Student Work to Promote Collective Inquiry. Journal of Mathematics Teachers Education, 7(3), 203-235.

Lamb, L. L., Bishop, J. P., Philipp, R. A., Whitacre, I., & Schappelle, B. P. (2018). A cross-sectional investigation of students’ reasoning about integer addition and subtraction: Ways of reasoning, problem types, and flexibility. Journal for Research in Mathematics Education, 49(5), 575 – 613. 

Lamb, L. L., Bishop, J. P., Philipp, R., Whitacre, I., Schappelle, B., & Lewis, M. L. (2012). Developing symbol sense for the minus sign. Mathematics Teaching in the Middle School18(1), 5–9.

Lamb, L. C., Philipp, R. A., Jacobs, V. R., & Schappelle, B. P. (2009). Developing teachers’ stances of inquiry: Studying teachers’ evolving perspectives.  In D. Slavit, T. Holmlund Nelson, & A. Kennedy (Eds.),Perspectives on supported collaborative teacher inquiry, (pp. 16–45).  New York: Taylor & Francis.

Lambert, R., & Sugita, T. (2016). Increasing engagement of students with learning disabilities in mathematical problem-solving and discussion. Support for Learning31(4), 347–366. https://doi.org/10.1111/1467-9604.12142

Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., Franke, M. (2010) Using designed instructional activities to enable novices to manage ambitious mathematics teaching (pp. 129-141).  In  M.K. Stein & L. Kucan (Eds.) Instructional explanations in the discipline.  New York: Springer.

Levi, L. & Ambrose, R. (2018). Cognitively Guided Instruction and Formative Assessment.In E. Silver and V. Mill (Eds.) A Fresh Look at Formative Assessment in Mathematics Teaching: Leveraging Connections to Tasks, Discourse, Equity, and More.Reston, VA: National Council for Teachers of Mathematics

Levi, L. (2004).  Are students in a reform mathematics class ill-equipped for traditional mathematics instruction?  Texas Mathematics Teacher, Spring 2004, 24 – 27.

Levi, L. (2000) Gender Equity in Mathematics Education.   Teaching Children Mathematics, October 2000.

Lubinski, C. A. (1994). The influence of teachers' beliefs and knowledge on learning environments. Arithmetic Teacher, 41(8), 476-479.

Lubinski, C. A., Mariani, A. N. (1999). Affecting K-9 teachers’ beliefs to improve instruction in mathematics. The Mathematics Educator, 4(1), 1-14.

Lubinski, C. A. & Jaberg, P. A. (1997). Teacher change and mathematics K-4:  Developing a theoretical perspective. In E. Fennema and B. Scott Nelson (Eds.), Mathematics Teachers in Transition  (pp. 223-254). 

Lubinski, C. A., & Otto, A. D. (2004). Preparing K–8 preservice teachers in a content course for standards-based mathematics pedagogy.  School Science and Mathematics, 104(7), 336-350. 

Lubinski, C. A., & Otto, A. D. (2004). How learning to make sense of mathematics in a content course can affect the beliefs of preservice teachers.  In Krauthausen, Günter & Scherer, Petra (Eds.), Mit Kindern auf dem Weg zur Mathematik: Ein Arbeitsbuch sur Lehrerbildung (pp. 92-100)Donauwörth: Auer.  (Invited chapter)

Maldonado, L., Turner, E. E., Dominguez, H. & Empson, S. B. (2009) English Language Learners Learning fromand Contributing toDiscussions. Mathematics for All: Instructional Strategies for Diverse Classrooms.National Council of Teachers of Mathematics.

Molina, M. and Ambrose, R. (2007) Fostering Relational Thinking While Negotiating the Meaning of the Equal Sign.  Teaching Children Mathematics, September 2006, p. 111 – 118.

Moscardini,L & Sadler, S. (2018). Scottish Attainment Challenge Cognitively Guided Instruction Project 2016-2018 Final Report. Glasgow, Scotland: University of Strathclyde. DOI: 10.13140/RG.2.2.21616.30728

Moscardini, L., (2015). Primary special school teachers' knowledge and beliefs about supporting learning in numeracy. Journal of Research in Special Educational Needs.15, (1), 37–47.  

Moscardini, L. (2014) Developing equitable elementary mathematics classrooms through teachers learning about children’s mathematical thinking: Cognitively Guided Instruction as an inclusive pedagogy. Teaching and Teacher Education, 43, 69–79. 

Moscardini, L. (2010). ‘I like it instead of maths’: how pupils with moderate learning difficulties in Scottish primary special schools intuitively solved mathematical word problems.  British Journal of Special Education, Vol 37Number 3.

Moscardini, L. (2009). Tools or crutches? Apparatus as a sense-making aid in mathematics teaching with children with moderate learning difficulties. British Journal of Support for Learning, 24,(1), 35-41. 

Neal, R. A. & Battey, D. (2014). Opening classroom spaces for the mathematical success of African American and Latino/a Students. TODOS Research Monograph, 3, 50-64.

Pateman, N., & Lubinski, C. A. (2004). Meeting the challenge of new mathematics standards in the United States: Two perspectives.  In Krauthausen, Günter & Scherer, Petra (Eds.), Mit Kindern auf dem Weg zur Mathematik: Ein Arbeitsbuch sur Lehrerbildung (pp. 101-109)Donauwörth: Auer. (Invited chapter)

Philipp, R. A.  (2008).  Motivating prospective elementary school teachers to learn mathematics by focusing upon children’s mathematical thinking. Issues in Teacher Education, 17(2) 7-26.

Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning(pp. 257-315). Reston, VA: National Council of Teachers of Mathematics.

Philipp. R. A., Ambrose, R. Lamb, L. L. C., Sowder, J., T., Schappelle, B. P., Sowder, L., Thanheiser, E., and Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge of prospective elementary school teachers:  An experimental study.  Journal for Research in Mathematics Education. (28)5, 438 – 476.

Philipp, R. A., & Thanheiser, E. (2010). Showing your students you care:  Seeing the individual trees in the classroom forest. New England Mathematics Journal, 42 (May, 2010), 8-17.

Pierson, J, Lamb, L, Philipp, R., Schappelle, B., & Whitacre, I. (in press). Children’s Reasoning about “Numbers UnderZero.” Teaching Children Mathematics.

Pierson, J., Lamb, L., Philipp, R., Schappelle, B., & Whitacre, I. (2010).A Developing Framework for Children’s Reasoning About Integers. In P. Brosnan, D. Erchick, & L. Flevares (Eds)Proceedings of the 32ndAnnual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 695-702).Columbus, OH: The Ohio State University.

Sahin, N. (2015). The effect of cognitively guided instruction on students’ problem solving strategies and the effect of students’ use of strategies on their mathematics achievement (Doctoral dissertation). University of Central Florida, Orlando, FL. 

Schoen, R. C., LaVenia, M., & Tazaz, A. M. (2018). Effects of the first year of a three-year CGI teacher professional development program on grades 3–5 student achievement: A multisite cluster-randomized trial. (Research Report No. 2018-25). Tallahassee, FL: Learning Systems Institute, Florida State University.

Schwerdtferger, Julie K., Chan, A. (2007). Counting Collections.  Teaching Children Mathematics, March 2007, p. 356 – 361.

Steinberg, R. M., Empson, S. B., Carpenter, T. P. (2004). Inquiry into Children’s Mathematical Thinking as a Means to Teacher Change.  Journal of Mathematics Teacher Education, 7(3), 237-267.

Turner, E., Celedon-Pattichis, S., Marshall, M. & Tennison, A. (2009). "Fíjense amorcitos, les voy a contar una historia":  The Power ofStoryto Support Solving and Discussing Mathematical Problems among Latino/a Kindergarten Students(pp. 23-43).  In D. White & J. Spitzer (Eds).Mathematics for Every Student: Responding to Diversity, Grades PreK-5 (pp. 19-42).Reston, VA: NCTM.

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.

Turner, E. & Celedon-Pattichis, S. (in press, April 2011) Problem Solving and Mathematical Discourse among Latino/a Kindergarten Students: An Analysis of Opportunities to Learn. Journal of Latinos in Education.

Turner, E. E., Junk, D., & Empson, S. B. (2007). The power of paper-folding tasks: Supporting multiplicative thinking and rich mathematical discussion. Teaching Children Mathematics,13(6), 322-329.

Warfield, J., & Yttri, M. J. (1999). Cognitively Guided Instruction in one kindergarten classroom. In J. V. Copley (Ed.). Mathematics in the early yearsReston, VA: NCTM.

Warfield, J. (2001). Where mathematics content knowledge matters: Learning about and building on children’s mathematical thinking (pp. 135-155). In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics.Mahwah, NJ: Lawrence Erlbaum Associates.

Webb, N. , Franke, M., De, T, Chan A., Freund, D., Shein, P., Melkonian, D. (2009).   “Explain to your Partner”:  Teachers’ instructional practices and students’ dialogue in small groups.   Cambridge Journal of Education.

Webb, N. M., Franke, M. L., Ing, M., Chan, A., De, T., Freund, D., & Battey, D. (2008). The Role of teacher instructional practices in student collaboration. Contemporary Educational Psychology, 33(3), 360-381.

Whitacre, I., Bishop, J. P., Philipp, R., Lamb, L. L., & Schappelle, B. (2014). Dollars and sense: Students’ integer perspectives. Mathematics Teaching in the Middle School,20(2), 84–89.

Whitacre, I., Bishop, J. P., Lamb, L. L., Philipp, R. A., Schappelle, B. P., & Lewis, M. L. (2012). Happy and sad thoughts: An exploration of children’s integer reasoning. Journal of Mathematical Behavior31, 356–365.

Whitacre, I., Bouhjar, K., Bishop, J. P., Philipp, R. A., Schapelle, B. P., & Lamb, L. L. (2016). Regular numbers and mathematical worlds. For the Learning of Mathematics36(2), 20–25.

Whitacre, I., Lamb, L., Azuz, B., Bishop, J. P., Philipp, R. A., & Schappelle, B. P. (2017). Integer comparisons across the grades: Students’ justifications and ways of reasoning. Journal of Mathematical Behavior45, 47–62.

Whitacre, I., Schoen, R. C., Champagne, Z., & Goddard, A. (2017). Relational thinking: What’s the difference? Teaching Children Mathematics23(5), 303–308.