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Fractions: The New Frontier for Theories of Numerical Development

http://eric.ed.gov/?q=10.%09Fractions%3a+The+New+Frontier+for+Theories+of+Numerical+Development&id=ED552807

This article discusses the connection between the understanding of fractions and the success in later math classes.  Many people struggle with fractions because they attach whole number properties to fractions, which is not true.   Also, most students struggle with the meaning of a fraction, which leads to incorrect answers.  The suggested intervention in this article relates to taking time to teach fraction magnitude.  That is the one area that has the most data to increase fraction understanding.

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The Effects of a Direct Instruction Program on the Fraction Performance of Middle School Students At-risk for Failure in Mathematics

http://mathenrich.pbworks.com/w/file/fetch/52432358/EffectsofaDirect.pdf

This article gives a detailed explanation of different interventions that can be used to build a stronger understanding of fractions.  The program used was based on the direct instruction model.  This is usually used with students who have learning disabilities.  In this case, it was used with students who were at risk for failing math.  Teachers used a variety of methods to teach the content. Data was collected through numerous assessments.  Students received both direct instruction as well as traditional instruction.  This allowed for the observers to see the students in both settings.  The highlight of this article is that the intervention was done without taking any time away from the regular classroom setting.  In addition, students were not allowed to move on to the next topic until mastery was established.

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WWC Review of the Report "Does Working Memory Moderate the Effects of Fraction Intervention? An Aptitude-Treatment Interaction." What Works Clearinghouse Single Study Review

http://ies.ed.gov/ncee/wwc/pdf/single_study_reviews/wwc_fuchs_121614.pdf

This article provided data to support intervention groups for help with fractions. The comparison group only received lessons provided by the teacher according to the text provided.  The students in the intervention group not only had the teacher led lesson, but were also pulled during the day for thirty minutes to receive more specific help; this included fluency, manipulatives, and supplement activities.

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Body Fractions: A physical approach to fraction learning

http://eric.ed.gov/?q=+Teaching+Fractions+in+Middle+Grades+Mathematics&pr=on&ft=on&id=EJ936533

This article gives a kinesthetic activity to help build understanding of fractions.  Students use their bodies to represent parts of fractions and work together to build different amounts.  This is definitely an activity that I would incorporate during my intervention plan.  Due to it being engaging, students tend to remember it better than just writing notes on the subject.  The author also offers a variation of the activity to use when moving to different topics.

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Figuring Out Fractions: One Teacher's Journey to Demystify Division of Fractions

http://web.b.ebscohost.com.library.marygrove.edu:2048/ehost/detail/detail?sid=1c37c846-36b7-435b-9ff9-89c52723beb0%40sessionmgr112&vid=6&hid=106&bdata=JnNpdGU9ZWhvc3QtbGl2ZSZzY29wZT1zaXRl#db=eft&AN=508157167

This article is written by a teacher who has had a personal revelation with fractions.  I enjoyed reading this because it put a lot of focus on teaching for understanding. Most teachers know how to multiply and divide fractions using the algorithm, yet cannot find the works to explain why it works.  The author makes the point that teachers should always be willing to learn, or relearn concepts to help provide a better learning experience.  Intervention for the students is essential, but teachers may also need an intervention.

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Instructional Coherence in Chinese Mathematics Classroom—A Case Study of Lessons on Fraction Division

http://eric.ed.gov/?id=EJ894385

This article discusses the idea of coherence in lessons created by teachers.  It goes on to give an in depth explanation of the four lessons taught.  The teacher, Mrs. X, used multiple components to address each lesson.  I noticed that Mrs. X took time to work through and discuss each problem, one at a time.  There was no rushing through the content.  The students were actively engaged and were required to give reasoning for their findings.  The article stresses the importance of connecting each new lesson to previous lessons.  I found that by connecting each of my fraction lessons together will help the students build on prior knowledge and increase their new understandings.

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Cognitive Models: The Missing Link to Learning Fraction Multiplication and Division

http://eric.ed.gov/?q=division+of+fractions&pr=on&ft=on&id=EJ811122

This article focuses on using a cognitive model when teaching multiplication and division of fractions.  There are visuals being used and it breaks it down into easy to follow steps.  There was an experimental group, which used the cognitive model and a control group that used the traditional methods for multiplication and division.   The data recorded shows immense gains for the experimental group.

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Do teachers and students understand the difference between conceptual and procedural knowledge?

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Working with Students to Help Them Understand Fractions

http://eric.ed.gov/?q=Teaching+Fractions+in+Middle+Grades+Mathematics&pr=on&ft=on&id=EJ818868

This article gives explicit examples of what one teacher did to help build an understanding of fractions in her classroom.  Karen Tanner assessed the situation, asked her students for their input, and modified lessons to build an understanding.  Tanner also mentions the importance of emphasizing procedural and conceptual knowledge.

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Improving At-Risk Learners’ Understanding of Fractions

http://eric.ed.gov/?q=Improving+At-Risk+Learners%27+Understanding+of+Fractions&pr=on&ft=on&id=ED552737

This article discussed an intervention program that was used to collect data to check for an increase in understanding of fractions.  Students were chosen based on WRAT-4 (Wide Range Achievement Test) scores and randomly placed either into the intervention group or the control group.  The article goes into detail to explain what took place during the intervention, as well as the data collected.

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Developmental and Individual Differences in Understanding of Fractions

http://eric.ed.gov/?q=developmental+and+individual+differences+in+understanding+of+fractions&pr=on&ft=on&id=ED552736

This article compared conceptual and procedural knowledge of fractions and the effect it had on low achieving and high achieving students.  Students who lacked conceptual knowledge tended to make more mistakes and rarely felt confident in their arithmetic.  The high achieving students showed more growth between sixth and eighth grade. These students also had deeper conceptual knowledge, making it easier for them to understand the procedures.  “Withoutknowledge of fraction magnitudes, fraction arithmetic, pre-algebra equation solving, and other aspects of middle school mathematics become arbitrary procedures that generate meaningless outcomes” (Siegler & Pyke, 2013, p. 1996).

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"Placing a greater instructional emphasis on the need to view each fraction as an integrated magnitude that expresses the relation between its numerator and its denominator might avoid subsequent difficulties not only in fraction arithmetic but in learning of mathematics more generally" (Siegler & Pyke, 2013, p. 200).

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Wall Street Journal

New Approaches to Teaching Fractions (Shellenbarger, 2013)

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The government is funding new research on more effective ways to teach the often-dreaded subject. So long, pie charts.

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What is the best method to teach division on fractions?

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Factors:

Teacher knowledge of fractions.

Hands on activities versus notes.

Teacher ability to teach same concept multiple ways.

Student ability to build fractions.

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Variables

Increase in scores on activities related to fractions.

Prior knowledge and exposure of fractions.

Feelings toward mathematics.

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Most students do not understand what fractions represent or how they are created.

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Students can learn new topics, such as solving multi step equations, but when a fraction is part of the equation, the students skip the problem entirely.

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Potential problem to research (topic):

Students struggle with complete math problems that involve the use of fractions.