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-Centers can include technology
-Centers should have a portion where students are working together
-Students should have choice in their centers
-Students should have an opportunity to meet in a small group with the teacher to work at own level

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Article 8 has a great table showing a center rotation schedule and what the students do.

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Article #10-Effects of Computer Technology on Math Learning

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Article #10-Effects of Computer Technology on Math Learning

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This study looked at 36, 793 students K-12 and how CT effected thier math learning. The study concludes that CT showed a greater impact on elementary students, special needs students, students that were being taught by a constructivist approach and students that took non-standardized tests versus standardized tests. This data shows me that a computer program could be a center choice for students in order to assist their math learning.

Li, Q. & Ma, X. Educ Psychol Rev (2010) 22: 215. doi:10.1007/s10648-010-9125-8

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A Meta-analysis of the Effects of Computer Technology on School Students' Mathematics Learning

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This study examines the impact of computer technology (CT) on mathematics education in K-12 classrooms through a systematic review of existing literature. A meta-analysis of 85 independent effect...

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This article discusses a school district that adopted a flipped classroom model due to old textbooks and no money. Although I am not wanting to do a flipped classroom model, I see how the advantages are similar to learning center advantages. Students are able to work at their own pace in the classroom, teachers can differentiate instruction, and students are held accountable for working independently.

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In fall 2009, the Byron School District near Rochester, Minn., faced a perfect storm of academic and financial challenges. Pushing from one direction was the dire need to order new high school math textbooks because the old ones were dog-eared and poorly matched to new state math standards. Pushing from the other direction was the reality that no funds were available. Two failed operating levy referenda had sunk the district to near the bottom in the state for local funding, and it was coming off a $1.2 million funding cut during the 2009-10 and 2010-11 school years. The district's annual budget for its 1,743 students--501 in the high school--is $18.1 million.

"We literally had no money for new textbooks," said then-Superintendent Wendy Shannon.

The math teachers stepped up to the challenge and came up with a radical idea: They would create their own curriculum, and, by bringing in online resources, do away with textbooks altogether. Thus was borne the bookless 24/7 math curriculum from which Byron High School's "flipped classrooms" emerged.

It was a crash course in innovation, given that the teachers hadn't even heard of flipped classrooms when they began the process. But they were determined to develop their own curriculum aligned to state standards and dedicated to finding the best solution for their students. Beginning in January 2010, they set to work, meeting before school from 6:45 to 7:45 a.m. every Monday during their professional learning community time. As they dissected the new math standards, reviewed student test data indicating areas of special challenge, and previewed resources pulled down from the web, they realized they couldn't just buy a prepackaged online math curriculum. First, they had no money to do this; just as important, any prepackaged curriculum--traditional or online--presented the same problems of not fully aligning with Minnesota's state standards. They would have to create an entirely new model.

To fuel their efforts, they landed a $5,000 grant from a local foundation, the Byron Fund for Excellence in Education, which provided small stipends for teachers to continue to work together during summer 2010 and paid for Kuta, a software tool for creating worksheets and tests. With the help of Jen Hegna, the district's technology director, the teachers used Moodle to create an online site for each course. Then, they realized they would need to record lecture videos so students and parents would have a resource for when they were at home in place of the books. And once they began to record lessons on an interactive whiteboard, uploading them onto YouTube, they realized that the students could view these lessons at home as homework, freeing up class time for discussion and practice.

As they worked, adopting some of the concepts of flipped classroom pioneers Aaron Sams and Jonathan Bergmann, they adapted the technique to fit their needs. They started small, experimenting with a few chapters and classes in fall 2010. Today, the innovation has spread to all math courses at Byron High. In addition, 8th-grade mathematics teacher Jeremy Baumbach, who joined the high school teachers in the redesign process, now provides some flipped classes for middle school students. Other departments also are watching and learning from their math colleagues. In fall 2011, Intel awarded Byron High School its School of Distinction Award for Mathematics.

Byron teachers share their top 10 reasons for adopting a flipped classroom.

#1. Students move at their own pace.

In a traditional classroom, the teacher lectures and demonstrates how to solve the math problems during the constraints of the class period. The teacher is doing the active work and the students are passively listening. For some students, the length of the class period is just right, but for those who understand the material, the lectures and questions can drag on and on. Conversely, for those who struggle, there isn't enough time left after a lecture for them to "get it. ...

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10 Reasons to Flip: A Southern Minnesota School District Flipped Its Math Classrooms and Raised Achievement and Student Engagement

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In fall 2009, the Byron School District near Rochester, Minn., faced a perfect storm of academic and financial challenges. Pushing from one direction was the dire need to order new high school math textbooks because the old ones were dog-eared and poorly matched to new state math standards.

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This article is an action research study on the effect of small groups on achievement in math for first graders. The findings show there are potential benefits to grouping students in small groups based on their math needs and also suggests more research needs to be done.

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"Studies have found that teaching children through guided play can be more effective than didactic instruction because it encourages children to take on an active role in their exploration" (Ramani & Eason, 2015).

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Article #7- Learning math through play and games

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Article #7- Learning math through play and games

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This article looks at preschool students and how playing specific games can increase their knowledge of basic math skills. For example, using a linear numerical board game can improve a child's numerical knowledge and sustain over time. This article gives great examples of games to play with students and how to make math time more play based.

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This study looked at five schools will varying levels of diversity and how learning centers affected student achievement. The study concludes that giving students the opportunity to work on learning centers that directly relate to the unit objectives increased student engagement. The study also recommends giving students freedom to choose which center they want to be at, freedom to work at their own pace, and having an effective transition system.

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An observational study of K learning centers

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Article #5- What Does Good Math Instruction Look Like?

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Article #5- What Does Good Math Instruction Look Like?

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This article was a great catalyst for what my math instruction and centers should consist of. It also reinforces the fact that students learn math best when working with others, working with manipulatives, solving challenging problems, and using various mediums to show and display work. It also talked about how good teaching is key, and gave me some ideas for how to ensure I'm doing my best work for my students.

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This article doesn't directly relate to my topic, but I found it useful. This study was conducted to see the effects of four main math curriculums on student achievement. They compared Math Expressions, Investigations, SFAW, and Saxon curriculums. All varied on level of student-centered and teacher-centered approaches. The only significant finding was that Math Expressions showed student achievement 0.11 standard deviations higher than Investigations and SFAW. They concluded that curriculum matters. Math expressions is a curriculum that is both student and teacher directed. Students explore and discuss questions related to math but are also taught explicit procedures.

Agodini, R., Harris, B., Thomas, M., Murphy, R., Gallagher, L., & National Center for Education Evaluation and Regional Assistance, (. (2010). Achievement Effects of Four Early Elementary School Math Curricula: Findings for First and Second Graders. NCEE 2011-4001.

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Math anxiety keeps popping up as I search for articles. I wonder if a lot of teachers have anxiety about teaching math? Might be interesting to look into the effects. This could be a bias in my study.
This is one example that says girls who have a teacher who has math anxiety have lower confidence in their abilities. Boys were unaffected.
Ornes, S. (2010, Feb 10). Teaching math, teaching anxiety. Science News for Kids, Retrieved from http://library.marygrove.edu:2048/login?url=http://search.proquest.com/docview/1113991104?accountid=28829

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This article focuses on a specific model of allowing students a set of choices, or a menu of multilevel tasks in math that takes place during the math block. Unfortunately I do not have access to read the entire article, but am requesting access.

Reference: Legnard, D. S., & Austin, S. L. (2012). The MENU for every young mathematician's appetite. Teaching Children Mathematics, 19(4), 228. Retrieved from http://library.marygrove.edu:2048/login?url=http://search.proquest.com/docview/1223475730?accountid=28829

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Article #2 Differentiated Instruction allow teachers to meet students needs

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Article #2 Differentiated Instruction allow teachers to meet students needs

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Another study was conducted to see how guided math and differentiated instruction impacted student learning. The study concludes that the teacher's ability to meet the students math needs were greatly improved with differentiated instruction and guided math.

John, Y. J., Joseph, S., & Sampson, A. (may 2014). PROSPECTIVE TEACHERS USING GUIDED MATH TO DIFFERENTIATE MATHEMATICS INSTRUCTION. International Journal of Research In Social Sciences,4(1), 64-76. Retrieved March 26, 2017, from www.researchgate.net.

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The problem with my math time is:
1. Students are mostly not engaged
2. Students lack ability to solve real-world problems, significant in common core.
3. Increased amount of behavior problems during math -- (I believe) due to lack of movement and choice.

I believe introducing math centers or "guided math" will help my students be more engaged and be more familiar with the concepts because they will be working with hands-on materials and solving problems with partners or groups.

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I found a study about technology improving math understanding. Technology could be a center I use. Our school already uses a program called Dreambox, which is a CAI (computer-assisted instruction)application and was found the be the best kind of application for improving understanding.

Cheung, A. C., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88-113. doi:10.1016/j.edurev.2013.01.001

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I plan to study the effect of math centers on student understanding of math concepts because I want to find out if increased movement and choice show an increase in student understanding so that I may better understand the most effective ways to teach math to first graders.