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This article explores the use of mathematical discourse, or misconceptions, to promote student discussions and learning. It goes on to examine the process and best practices of using mathematical discourse to teach students content and practice mathematical vocabulary skills.

This article details how to establish mathematics discourse in the classroom. The article details specific steps to model, scaffold, and encourage mathematics discourse between students throughout a math block. Discourse supports collaboration, justification of ideas, and flexibility with mathematical thinking. The article is geared towards elementary students; however, the ideas are universal for all grades.

This article helps teachers create a friendly and safe math community. Students will be able to use math vocabulary to explain their thinking and reasoning when solving a problem.

Meta-analysis was conducted on interventions used for mathematics with students with learning disabilities. There were four instructional components examine to determine their effectiveness and impact -- a) approached to instruction and/or curriculum design, b) formative assessment data and feedback to teachers, c) formative assessment data and feedback to students and d) peer-assisted mathematics instruction. The research indicates the positive impact of cognitive strategies and the direct instruction model for mathematics instruction. The information was beneficial. Direct instruction often used for reading instruction of students with disabilities so it only makes sense that is also works for math instruction. Research-based information helps me determine what instructional strategies and practices I will include in my classroom.

(Week 7: Jeremy, Kelly, Patience and Sherita) This article is originally a Diigo share from 2015. This journal article is accessible in the link given above. This journal article discusses how here in America, there is a pervasive fear surrounding teaching and learning math. The author suggests that the American public suffers from innumeracy. Through discussing the article, the group agrees that many countries have mastered the use of American mathematical principles. The article discussed that by utilizing and engaging in clear mathematical methods of learning for students and by creating valuable conversations, making the learning process more viable, the students consequently, learn. "Instead of having students memorize and then practice endless lists of equations - which Takahashi remembered from his own days in school - Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math's procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun." (Green, 2014) Teachers can use this article to further their instructional practices by utilizing math in a real world format, in a conversational and hands on applicable manner, making learning math fun and interesting for their students. In some instances, math classes may be seen as boring and monotonous tools that serve to be an overtly unloved subject area here in America. The simple truth, is that many teachers love to learn and teach math here in America, and there is a realization for teachers, that all nations compete mathematically. In technology, industry, trade, consumerism and capitalism, numbers and mathematical data maintain a lot of the privile

Week 9: Melissa and Claire This journal article is accessible thought the link given above by accessing the UMUC library This article was about how a randomized experimental design was used to examine the effects of a digital formative assessment tool on mathematics achievement and motivation in the classroom. Experimental schools used a digital formative assessment tool while control schools used their regular teaching methods and materials. The data used included standardized achievements pre-posttest data, student motivation survey data, classroom data observation data, and student log files. The results of the tests revealed positive effects on student achievement and motivation. The digital formative assessment tool positively impacted achievement and motivation. It also helped teachers to differentiate instruction. The more the students used the digital tool the higher their achievement and motivation for mathematics improved. Reference: The effects of a digital formative assessment tool on mathematics achievement and student motivation: Results of a randomized experiment By: Janke M Faber, Hans Luyten, Adrie Visscher Doi:10.1016/j.compedu.2016.12.001

Additional information about milestones and K-12 math curriculum is available on The National Council of Teachers of Mathematics Web site. NCTM's Principles and Standards for School Mathematics outlines grade-by-grade recommendations for classroom Mathematics instruction for both content matter and process.

Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency.

This article reports the results of a study of grade 2 students 7 - 8 years old) using game technology versus paper/pencil games and the effects of increased use of game technology on assessments. The study found that the students using the game technology had increased performance and that increased use of technology also increased student performance. Shin, N. Sutherland, L. M., Norris, C. A., & Soloway, E. (2012). Effects of game technology on elementary student learning in mathematics. British Journal of Educational Technology, 43(4), 540-560. doi:10.1111/j.1467-8535.2011.01197.x

In this study, researchers are looking at the impact of Math Snacks on student achievement in Mathematics. Nine teachers in 2 districts took part in this research. The results showed that when teachers used Math Snacks and the materials in the program, there was a positive impact on student achievement. However, because of the small sample size, the results cannot be generalized.

Week 9: This is a journal article that ties in the importance of screencasts and mathematical education. The article delves deeper into e-learning and evaluates the effectiveness of screencasts on both math and science. Screencasts can be used as instructional strategies for increasing learning beyond what an individual educator can do for any one child at a time. The key behind this strategy in its value is if it is reused enough times to impact learning. It is a resource to keep in mind when planning for reteaching or providing more exposure and support for a concept learned.

I selected this article because I was curious to learn how the authors investigated the student achievement issue with their student centered (experiment) group and a teacher centered (control) group comparison study; all while being supported by the curriculum, teachers, and professional development. The student centered group engaged in the use of drill and practice of computation based on the school's mathematics curriculum, in addition to an introduction to the use of presentation software. Meanwhile the control group focused only on the teacher instruction. Moreover surprisingly based on the results of the study, the students involved in the Computer-Assisted Instruction (CAI) experiment group did not have a statistically significant positive influence on student achievement. Jennifer Smith

The following is a pdf file about how to integrate writing into mathematics. It is a fantastic resource from the Michigan Department of Education that addresses integrating Common Core skills into every subject area.

Smith points out that although children learn to count, they may not understand the concept of number. He posits that the world of mathematics must be entered, explored, and used principally through reason and that only a few mathematical concepts are learned via the senses or spoken language

This software is a game-based program that works on many areas in mathematics. the targeted grade levels are 1-5. I have used the software, and I found myself on it longer than expected. for the most part, I liked how the software is designed. I appreciate the gaming aspect of the software. It doesn't make you feel like you're just doing math work to do. I believe that the only thing that i wasn't to big on was that it doesn't really separate the different grade levels. They do breakdown the different math areas. Overall I would recommend this software.

This article provides a literature review on studies that have been completed to look at the impact of Computer Technology and Math learning. This review looked at 46 studies that were conducted. The results overall showed a positive effect when Computer Technology was being used. However, the study also points out that when using CT, it must be combined with good teaching in order to maximize student understanding and learning.

As stated by the MobyMax software program, it "combines curriculum resources like placement tests, adaptive lessons, progress monitoring, IEP reporting with teacher tools, and motivational features (badges, games, and contests)." Users are able to upload student rosters for this program that accommodates grade levels k-8. Drill-and-practice lessons/assessments are Common Core State Standard aligned for both mathematics and reading content. My students and I enjoyed this software as a supplement to classroom instruction. With kid-friendly visuals and quick feedback on assessment scores, this classroom supplement will make learning more engaging.

DimensionU creates engaging and interactive multi-player video games that focus on core skills in mathematics and literacy. Our content aligns with the Common Core, state standards and classroom instruction Learn More about DimensionU Comprised of four engaging, multi-player games with access to curriculum in both Math and Literacy, grades 3 - 9. Some available games: * Meltdown is the DimensionU game that offers students a second chance when answering difficult questions, and rewards creative strategies to achieve victory. * Velocity is DimensionU's high-speed obstacle course that ensures players answer questions correctly in order to continue progressing through the race.

Note: The article is in English, although the page that shows the full article is written in Spanish. This article presents the idea that using screencasts and/or video lessons can help give students access to better instruction. The main idea of the paper is that to properly support students, one needs to be able to help answer questions in a timely fashion. As students study away from school, they tend to email questions to their instructors. I have noticed in recent years that emailed questions, although extremely relevant, can be unwieldy to explain via text. The article's text has the exact same conclusion (which is why it resonated with me the way it did) and makes the distinction that those same unwieldy or impractical 'text' solutions would be trivially answered if the student was face-to-face with the instructor. This concept, that face-to-face interaction is superior to all others, is the motivation for writing this paper. While screencasts and videos are not very interactive (for the most part), they are superior to simple written explanations (especially for complex or visual problems in science and math).

Wow! What a thoughtful analysis of the idea of using screencats and/or video lessons to support student learning.

Phet is a website that provides interactive simulations for science and mathematics. The simulations can be downloaded or used online for instructional, homework or review purposes. They are free and easy to use and a great learning device. An instructor can use the simulations to introduce information to students as well as using them as instructional methods to help students grasp ideas. Having students work on simulations in class or as homework can help enrich understanding.

this is a "protocol students can use to share and gain knowledge in preparation for an assessment."

I would rate the Go Go Mo protocol a 4 in the Rigor and Relevance dimension. While using this protocol, students are not only thinking (when they are giving) but also working. Students are actively moving around the classroom seeking out others from whom they can get new information. The teacher also suggested that they take their readings with them, which may hint at the fact that may still need to actively search for information. My group's SMART goal is that students will be able to analyze word problems to identify mathematical components needed to solve complex word problems and apply them to real-life problems and scenarios. This method could be effective (may be used on a smaller scale with 2-3 people for word problems) in that all students will have to identify information that they deem important and share with their classmates. From here, they can begin to decide what information is actually most important to solving the problem that is proposed and work together to solve the problem.

This activity will help close the learning gap by enabling collaboration and information sharing between students prior to exams.