Students Learn Mathematics With Deeper Meaning Essay

Students Learn Mathematics With Deeper Meaning Essay

Length: 1074 words (3.1 double-spaced pages)

Rating: Better Essays

Open Document

Essay Preview

Students learn mathematics with deeper meaning when they engage in productive struggle--grappling to make sense of problems (Hiebert & Grouws, 2007). Warshauer (2014) adds that teachers can engage students in productive struggle by asking them questions instead of telling them the answers; questioning can help students organize their thoughts as they struggle to make sense of problems. Teachers should increase the cognitive load by refraining from giving students too much help when solving problems (Hiebert & Grouws).
Granberg (2016) distinguishes between productive struggle and unproductive struggle; the latter she explains occurs when “their struggles did not provide any useful knowledge for solving the problem” (Journal of Mathematical Behavior, p. 44). She found that the students in her study were engaged in unproductive struggle initially, and all but two were able to convert from unproductive struggle to productive struggle. These two perhaps could not tap into their previous knowledge to construct new knowledge because the problems were too challenging and outside of their zone of proximal development. Granberg concludes that teachers should discuss with their students the differences between productive and unproductive struggle.
Granberg (2016) suggests that students may not engage in productive struggle if the problems are outside of their zone of proximal development. However, some students, such as ELLs, may not engage in productive struggle not because the mathematics is outside of their zone of proximal development, but because they struggle to make sense of problems in monolingual classrooms. Murrey (2008) explains that it may be necessary to provide ELLs with access to content by scaffolding the English, but the ma...

... middle of paper ...

...otsky maintains that students learn best when they are trying to solve problems that are too challenging for them to solve on their own but possible for them to solve with appropriate supports. The National Council of Teachers of Mathematics (2014) states that it is imperative for teachers to have high expectations for all students so they provide them problems that are within this zone. They say that too often teachers have low expectations for certain students and offer these students mathematical problems below their zone of proximal development. Teachers who have low expectations for students also tend to wait less time for those students to make sense of problems and persevere to solve them (Kilpatrick et al., 2001). Therefore, it seems apparent that students will be more successful if their teachers have high expectations for their capabilities in mathematics.

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

Graduation Speech : Elementary Mathematics Teachers

- At Neal Elementary mathematics teachers do not have an understanding of fact fluency and do not provide opportunities for students to develop fact fluency in their classroom learning experiences. After speaking with several stakeholders, there appears to be a lack of understanding of what fluency means and how to build fluency within students. During conversations it is evident that students on my campus often practice their multiplication facts by taking timed tests. The majority of the stakeholders I spoke with suggested that they place a strong emphasis on students memorizing facts and use timed tests....   [tags: Education, Mathematics, Teacher, School]

Better Essays
1196 words (3.4 pages)

“Writing to Learn” in a Math Classroom Essay

- Theory of “Write to Learn” Reading and writing are the basis of the original meaning of literacy. This definition, however, changed over time and culture. The term has expanded to include computer literacy, digital literacy, information literacy, health literacy, etc. (Vacca, Vacca, & Mraz, 2011). Nevertheless, the most important change to the term literacy is expanding the use of reading and writing. Literacy is defined as understanding, thinking and practicing the use of language in different cultural/social settings through the use of all types of media which allows people to communicate and make meanings (Vacca et al., 2011)....   [tags: Education, mathematics]

Better Essays
891 words (2.5 pages)

The Importance Of Students Learn And Grow Academically Essay

- To ensure that students learn and grow academically, it is very important that they skillfully learn how to read and write. In fact, students in kindergarten through third grade, must be in an environment that enables them to learn strategies to improve their reading and writing skills. This topic is very interesting and personal to me because my daughter, Goldie, is in third grade. Last year, I found out that she and the other third grade students are required to take and pass the standardized reading assessment, AZ Merit, in order to be promoted....   [tags: High school, Educational years, Third grade]

Better Essays
1180 words (3.4 pages)

The Positive Effects Of The Common Core 's Mathematics On American Students

- Morgan Williams Professor Stallcup VTMA 111-L 28 October 2014 The Positive Effects of the Common Core’s Mathematics on American Students The Common Core has been a highly debated educational initiative based in the United States that provides children of all race, religious denomination, and socioeconomic background the same educational path from kindergarten through senior year of high school or the 12th grade. The Common Core provides six standards on its website that serve as its oath. “The standards are: 1....   [tags: High school, Education, Standardized test, Teacher]

Better Essays
1767 words (5 pages)

Important Aspects of Teaching Mathematics Essay

- Teaching mathematics has evolved from the traditional instrumentalist view where the focus is on knowledge mathematical facts, rules and methods as independent concepts, to the more contemporary constructivist approach which focuses on building on prior knowledge and experiences incorporating mathematical facts, rules and methods to problem solve and investigate new mathematical concepts. This will in turn, enable students to apply concepts in real life situations. Teaching thematically is an approach which allows concepts to be applied to real life situations....   [tags: math Education, math, teachers]

Better Essays
1430 words (4.1 pages)

Cooperative Learning in Mathematics Essay example

- Cooperative Learning in Mathematics Low test scores and lack of motivation in mathematics by students in grade school is an issue that has recently been put under the spotlight. According to a study done in 2003, mathematics achievement levels in the United States are much lower than those in other developing countries. The results of this study show that the US is ranked 15th among the 47 participating countries in the 2003 NAEP Mathematics vs. TIMSS Mathematics for At or Above Proficient with 28.8% of students at or above the proficient level (Hambleton, 387)....   [tags: teaching strategies]

Better Essays
886 words (2.5 pages)

Essay about Information about Mathematics

- Research on and information about mathematics and the learning of mathematics has evolved over the last one hundred years. In the first half of the 20th century much of the focus was on computational approaches such as drill and practice and incidental learning (Brownell, 1947; Thorndike, 1924). This emphasis can certainly be attributed to the lack of technology available along with the needs of society for efficient computation (Jones et al., 2002). The development of the new math in the second half of the 20th century was a positional change for mathematics educators and researchers....   [tags: Education, Vygotsky, Lesh, Dienes, math]

Better Essays
1064 words (3 pages)

Technology in Mathematics Classrooms Essay

- Technology Views NCTM summarizes the technology principle by saying, “technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” I’m not sure that I agree with the entirety of this statement. Technology is important; it allows students to quickly make connections that would be lost without the speed and precision of computers. Technology also allows for thoughtless reproduction of facts already known. Imagine how long it would take to solve a college level mathematics problem without the aid of calculators for division, multiplication, exponents, and logarithms....   [tags: Education School]

Free Essays
893 words (2.6 pages)

A World Without Mathematics Essay

- According to teachers for as long as any can remember, one cannot survive in this world without mathematics, yet thousands in the United States alone cannot grasp mathematics, cannot learn mathematics because of “Dyscalculia” (also called Dyscalcula). Dyscalculia is a term meaning "specific learning disability in mathematics." People who suffer with a poor memory for all things mathematical have many other symptoms and characteristics. Taken as a whole, these coexisting conditions comprise what is termed as "the dyscalculia syndrome." Dyscalculia is an MLD (mathematics learning disability) that affects approximately ten percent of the US population, yet almost no one (sh...   [tags: essays research papers]

Free Essays
903 words (2.6 pages)

Understanding Mathematics Essay

- Understanding Mathematics This paper is an attempt to explain the structure of the process of understanding mathematical objects such as notions, definitions, theorems, or mathematical theories. Understanding is an indirect process of cognition which consists in grasping the sense of what is to be understood, showing itself in the ability to apply what is understood in other circumstances and situations. Thus understanding should be treated functionally: as acquiring sense. We can distinguish three basic planes on which the process of understanding mathematics takes place....   [tags: Math History Learning Papers]

Better Essays
3992 words (11.4 pages)