**Literature Review**

EDC 380R: Educational Research and Design

Cinthia Chen

EDC 380R: Educational Research and Design

Cinthia Chen

THE LITERATURE

IMPLICATIONS FOR RESEARCH AND PRACTICE

**THE RESEARCH QUESTION**

First, a math problem...

Maria had 15 stickers. Her teacher gave her 17 more. How many does she have now?

THE ARGUMENT

Number sense is a major topic in mathematics curriculum (NCTM, 1989).

Number sense is an understanding of numbers and operations, "with the ability to

develop useful, flexible and efficient strategies for handling numerical problems (Yang, 2003)".

Children initiative, choice and curiosity develop positive disposition and persistence in math thinking (Wakefield, 1997).

Inquiry in mathematical thinking leads to deeper conceptual understanding of numbers.

THE FRAMEWORK

REFERENCES

Barlow, A. T., & McCrory, M. R. (2011). 3 Strategies for Promoting Math Disagreements.

Teaching Children Mathematics, 17(9), 530-539.

Boonen, A. J., Kolkman, M. E., & Kroesbergen, E. H. (2011). The relation between

teachers' math talk and the acquisition of number sense within kindergarten classrooms. Journal of school psychology, 49(3), 281-299.

Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A

longitudinal study of invention and understanding in children's multidigit addition and subtraction. Journal for Research in Mathematics Education, 3-20.

Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during

whole-group discussions. Journal of Mathematics Teacher Education, 14(5), 355-374.

Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children's mathematical

thinking in everyday mathematics classrooms. Journal for research in mathematics education, 148-170.

Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher

questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392.

Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components

of a math-talk learning community. Journal for Research in Mathematics Education, 81-116.

Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to

mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88.

Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to

promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203-235.

Kostos, K., & Shin, E. K. (2010). Using math journals to enhance second graders’

communication of mathematical thinking. Early Childhood Education Journal, 38(3), 223-231.

Mohamed, M., & Johnny, J. (2010). Investigating number sense among students. Procedia-

Social and Behavioral Sciences, 8, 317-324.

National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.

Varol, F., & Farran, D. (2007). Elementary school students’ mental computation proficiencies.

Early Childhood Education Journal, 35(1), 89-94.

Wakefield, A. P. (1997). Supporting math thinking. The Phi Delta Kappan, 79(3), 233-236.

Wheatley, G. H. (1992). The role of reflection in mathematics learning. Educational Studies in Mathematics, 23(5), 529-541.

Yang, D.C. (2003). Teaching and Learning Number Sense – An Intervention Study of Fifth

Grade Students in Taiwan. International Journal of Science and Mathematics Education. 1:115-134.

Future research will provide additional insight into children's mathematical thinking and help teachers design the learning experiences that will foster deeper understanding in this area.

Number sense competency in early elementary grades is a strong predictor of math achievement in testing grades, especially in problem-solving (Jordan, Glutting & Ramineni, 2010). This leads to opportunities for early intervention.

Children develop deeper mathematical thinking when...

they disagree and articulate their thinking to others. Dialogue leads to reasoning and sense making (Barlow & McCrory, 2011).

they write about and demonstrate their thinking process (Kostos & Shin, 2010).

hear teacher math talk. Teacher math talk stimulates the acquisiton of number sense skills in young children (Boonen, Kolkman & Kroesbergen, 2011).

they are given authentic problem-solving situations (Wakefield, 1997).

they engage in problem-centered learning that is inquiry based. This allows the teacher to use student thinking to guide instruction (Wheatley, 1992).

Inquiry-based Learning

Problem-based Learning

The Advancing Children's Thinking (ACT) framework (Fraivillig, Murphy & Fuson's study in 1999).

Students are able to do computation with algorithms, but struggle to understand the meaning of numbers and operations, number relationships and composition (Mohamed & Johnny, 2010).

FURTHER QUESTIONS

Inquiry based learning includes problem-centered learning. What would that look like during math instruction?

Will children engage in math inquiry without teacher modeling?

How can inquiry be fostered as students rely increasingly on school-learned strategies (using algorithms)?

Eliciting Children's Solution

Methods

Supporting Children's

Conceptual Understanding

Extending Children's Mathematica Thinking

How is the knowledge and understanding of number sense affected when second grade students participate in inquiry-based math instruction?