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What is Eureka Math?
What is Eureka Math?
Today’s mathematics classrooms are changing with the push for concrete representation and modelling. The mathematics curriculum used in Guilford County Schools for elementary students in grade K-5 is Eureka Math. This curriculum is grounded in fluency and the use of intentional learning progressions. It is a common core aligned curriculum that, “equates mathematical concepts to stories, with the aim of developing conceptual understanding” (Williams, 2015).
According to Williams, the program encourages students to use various mental strategies to solve and to focus on the process instead of the product which is very different from previous expectations. With this change the focus isn’t on simply getting the right answer but understanding the process and utilizing multiple modes of representation to obtain the same result. This for both parents and students can be frustrating as now many parents refer to the methods described in Eureka as “New Math” (Williams, 2015).
As described in the article Eureka Math is believed to “simply teach children to multiply those and larger numbers using pictures and other models, before they begin to stack one number atop another and carry over from the ones place to the tens place”. Although well intentioned, this can cause frustration and disinterest when students struggle with homework and parents are unable to help because they lack the background knowledge to give “appropriate feedback” (Vidya Thirumurthy, 2014).
The Reason for "New Math"
The Reason for "New Math"
CRA: Concrete Representational Abstract
CRA: Concrete Representational Abstract
The CRA method of instruction is composed of three components.
- The use of hands-on activities with manipulatives. Students become active participants in their learning and are able to link new abstract information to, “already solidified and personally meaningful networks of knowledge” when activities are well planned and intentional (Stein & Bovalino, 2001).
- The use of visual representations which connect to the use of manipulatives to create stronger foundational skills. These can take the form of pictorial representations, graphic organizers or virtual representations (Morin & Agrawal, 2016).
- Students can comprehend and solve problems without the use of those concrete and representational scaffolds mentioned above.
The goal of CRA is to develop a clear link between procedural and conceptual knowledge by providing the why behind the procedure prior to teaching it.
The goal of CRA is to develop a clear link between procedural and conceptual knowledge by providing the why behind the procedure prior to teaching it.
Theoretical Perspective for this Tool Kit
Theoretical Perspective for this Tool Kit
Constructivism brings value to the development of students’ personal mathematical ideas and connections. Students under this theory of instruction are encouraged to think for themselves and use their own methods for problem solving. Teaching using constructivism requires teachers to offer tasks and opportunities to focus students’ attention (Bruner, 1966). According to Moch, manipulatives and structured activities can be utilized in meaningful ways to help students develop well-grounded and interconnected understandings of mathematical ideas. Moch has also noted that activities planned by teachers that require manipulatives have also proven to be beneficial for regular students and inclusion students (2002).
These theories will guide the support and materials I include for homework support by not only providing manipulatives but also including structured activities. Along with the physical manipulatives and written activities I am also including videos that clearly explain what should be done. This would ensure that they are done correctly and will remove room for error due to differences in interpretation. The purpose would be to extend manipulative use into the home and provide parents with the tools to participate in meaningful enrichments activities at home. These enrichments activities should bridge school to home and allow students to explore the concepts and skills they are currently learning.
References
References
Boaler, J., & Chen, L. (2016, April 13). Using fingers to count in math class is not 'babyish'. Retrieved February 05, 2020, from https://www.theatlantic.com/education/archive/2016/04/why-kids-should-use-their-fingers-in-math-class/478053/
Boaler, J., & Dweck, C. S. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass, a Wiley Brand.
Bruner J. (1966). Toward a theory of instruction. Cambridge, MA: Belknap Press of Harvard University Press.
Burns, M. (2015). About teaching mathematics: A k-8 resource. Sausalito, CA: Math Solutions.
End-of-Grade Mathematics Tests at Grades 3–8 North Carolina Test Specifications. (2020, February 11). Retrieved March 2, 2020, from https://files.nc.gov/dpi/documents/files/test-specifications-eog-mathematics-2020-02-11.pdf
Flores, M. M., Hinton, V. M., & Taylor, J. J. (2018). CRA fraction intervention for fifth-grade students receiving tier two interventions. Preventing School Failure: Alternative Education for Children and Youth, 62(3), 198-213. doi:10.1080/1045988x.2017.1414027
Kennedy, L. M. (1986). A rationale. Arithmetic Teacher, 33, 6-7, 32.
Marley, S. C., Selig, J. P., & Carbonneau, K. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380-400. doi:10.1037/a0031084
Moch, P. L. (2002). Manipulatives work! The Educational Forum, 66(1), 81-87. doi:10.1080/00131720108984802
Morin, L. L., & Agrawal, J. (2016). Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with mathematics disabilities. Learning Disabilities Research & Practice, 31(1), 34-44. doi:10.1111/ldrp.12093
National Council of Teachers of Mathematics. (2000). Standards & focal points. Retrieved from http://www.nctm.org/standards/default.aspx?id=58
Parent Tip Sheets Grade 4. (n.d.). Retrieved February 12, 2020, from https://greatminds.org/download_pages/parent_tip_sheets_grade_4?opened_product_id=782
Post, T. R., Delmas, R. C., & Cramer, K. A. (2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111. doi:10.2307/749646
Sallee, B., & Rigler, N. (2008). Doing Our Homework on Homework: How Does Homework Help? The English Journal, 98(2), 46-51. Retrieved February 5, 2020, from www.jstor.org/stable/40503382
Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498. doi:10.2307/749423
Standards for mathematical practice. (n.d.). Retrieved February 12, 2020, from http://www.corestandards.org/Math/Practice/
Stein, M. K., & Bovalino, J. W. (2001). Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School, 6(6), 356-359. Retrieved from http://libproxy.highpoint.edu/login?url=https://search.proquest.com/docview/231301950?accountid=11411
Thirumurthy, V. (2014). Homework, homework EVERYWHERE: Indian parents' involvement with their children's homework. Childhood Education, 90(2), 83-90. doi:10.1080/00094056.2014.889497
Utilizing eureka math for successful knowledge building. (n.d.). Retrieved February 09, 2020, from https://greatminds.org/math/blog/eureka/post/knowledge-building-for-long-term-success-math
Valentine, J. C., & Cooper, H. (2001). Using research to answer practical questions about homework. Educational Psychologist,36(3), 143-153. doi:10.1207/s15326985ep3603_1
Van de Walle, J. A., Karp, K., Bay-Williams, J. M., Wray, J. A., & Brown, E. T. (2013). Elementary and middle school mathematics: Teaching developmentally. NY, NY: Pearson.
Williams, J. (2015, March 13). Inside eureka math: Does a popular common core math curriculum move too fast for young students? Retrieved February 17, 2020, from https://hechingerreport.org/inside-eureka-math-does-a-popular-common-core-math-curriculum-move-too-fast-for-young-students/
Xu, J., & Yuan, R. (2003). Doing homework: Listening to students,' parents,' and teachers' voices in one urban middle school community. School Community Journal, 13(2), 25-44. Retrieved from http://libproxy.highpoint.edu/login?url=https://search.proquest.com/docview/195462562?accountid=11411
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