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"Educational and developmental psychologists have tried to understand how skills and motivation are linked to academic achievement. While research supports ties between individuals' concepts of their abilities and their achievement, we lack a complete picture of how these relations develop from childhood to adolescence. A new longitudinal study looked at how youths' self-concepts are linked to their actual academic achievement in maths and reading from middle childhood to adolescence. The study found that students' self-concepts of their abilities in these two academic domains play an important role in motivating their achievements over time and across levels of achievement."

" The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks designed to observe what students do as they construct meaning. APOS Theory was used as a framework for analysis of growth. APOS Theory is a useful theoretical framework for studying and explaining conceptual development. Closely linked to Piaget's notions of reflective abstraction, it begins with the hypothesis that mathematical activity develops as students perform actions that become interiorized to form a process understanding of the concept, which eventually leads students to a heightened awareness or object understanding of the concept. Prior to any investigation, the researcher must provide an analysis of the concept development in terms of the essential components of this theory: actions, process, objects, and schemas. This is referred to as the genetic decomposition. The results of this study suggest a framework that a learner may use to construct meaning for logarithmic concepts. Using tasks aligned with the initial genetic decomposition, the researcher made revisions to the proposed genetic decomposition in the process of analyzing the data. The results indicated that historical accounts of the development of this concept might be useful to promote insightful learning. Based on this new set of data, iterations should continue to produce a better understanding of the student's constructions. " (from the abstract)

NSDL Science Literacy Maps are a tool for teachers and students to find resources that relate to specific science and math concepts. The maps illustrate connections between concepts as well as how concepts build upon one another across grade levels. 

"Math games are a great way to help students improve their math facts accuracy. These games can be general math or focus on a specific math concept such as, solving integers. One math game is called "Fraction Face-Off." This game can also be modified to address a varied of math concepts."

Still, in today's standard-driven classrooms, math homework is more complex than ever and math homework is usually a daily event. It is very important for a student to learn the basic concepts in math before going for any math homework and for the same quality tutoring is guaranteed. The Internet is a great medium for this purpose. Math homework help services on the internet through their expert advice on the exact concepts you are working on, are just a click away 24/7.

"The Middle School Stream aims to motivate and engage middle school students (grades 5 through 8) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The High School Stream aims to motivate and engage high school students (grades 9 through 12) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The Collegiate Stream challenges emerging game developers at the graduate and undergraduate levels to design video games for children (grades pre-K through 8) that teach key STEM concepts and foster an interest in STEM subject areas. The Educator Stream challenges educators to design video games for children (grades pre-K through 12) that teach key STEM concepts and foster an interest in STEM subject areas."

Does Understanding the Equal sign Matter? Examines several of the important concepts in algebra focusing on the concept of equality

"Usually, being able to visualise mathematical concepts to students is an important step in helping them understand techniques to illustrate connections with previous learning, helping them master maths notions to progress their skills. The importance of visualising concepts is clearly integral for Peter Mattock who has collected together a valued resource of mathematical activities that can be used with manipulative across the age and ability range."

It would be interesting to build a set a links to similar research results as this and discuss the implications this has for what we do as math teachers in our classrooms.

New research from Vanderbilt University has found students benefit more from being taught the concepts behind math problems rather than the exact procedures to solve the problems. The findings offer teachers new insights on how best to shape math instruction to have the greatest impact on student learning.

This just confirms what all the other research has been saying. The issue is getting all of us who didn't learn math conceptually, and who were not trained in college conceptually, to teach this way.

A collection of resources using poetry to teach math concepts

According to Nancy Kimberly of HASTAC, this set of video games won the 1st National STEM Video Game Challenge: "Numbaland!, produced by graduate students Derek Lomas of Carnegie Mellon University, Dixie Ching of New York University and Jeanine Sun of the University of California at San Diego, was the winner of the Collegiate and Impact Prizes and will receive $50,000 in total. The collection of four games allows children in kindergarten to grade 4 to construct a set of skills that helps develop their sense of number concepts"

With Glean PEMDAS (Please Excuse My Dear Aunt Sally), we present a math learning environment to help teachers extend students' understanding of order of operations concepts.

With Glean PEMDAS (Please Excuse My Dear Aunt Sally), we present a math learning environment to help teachers extend students' understanding of order of operations concepts. Glean PEMDAS can be used to introduce Order of Operations, and is best applied to critical inquiry about application of order.

From the National Center of Education Statistics: "The Trends in International Mathematics and Science Study (TIMSS) 2011 is the fifth administration of this international comparative study since 1995 when first administered. TIMSS is used to compare over time the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and science curricula in the participating countries. The results, therefore, suggest the degree to which students have learned mathematics and science concepts and skills likely to have been taught in school. In 2011, there were 54 countries and 20 other educational systems that participated in TIMSS, at the fourth- or eighth-grade level, or both. The focus of the report is on the performance of U.S. students relative to their peers in other countries in 2011, and on changes in mathematics and science achievement since 2007 and 1995. For a number of participating countries and education systems, changes in achievement can be documented over the last 16 years, from 1995 to 2011. This report also describes achievement within the United States by sex, race/ethnicity, and enrollment in public schools with different levels of poverty. In addition, it describes achievement in nine states that participated in TIMSS both as part of the U.S. national sample of public and private schools as well as individually with state-level samples of public schools."

From the abstract: "this study investigated how the perspectives of the non-computer science educators changed after learning game-programming and how it could be fitted into the K-12 curriculum. Fourteen non-computer science educators and/or administrators in the K - 16 educational systems who made up a cohort at Sam Houston State University, Master of Education/Instructional Technology Program participated in this study. The participants were required to learn two free Web 2.0 game-programming applications and reflect on an article related to reviving interest in math and science as part of their program. Qualitative data consisted of online reflections, and peer-review processes through Facebook. A quantitative component was added to the analysis. The findings indicated that: (a) the perspectives of the participants changed from negative to positive as they reflected on their own game-programming learning experiences; (b) participants came to understand how game programming could build up students' logical concepts and critical thinking skills improving performances in math, science, and other subjects; and (c) due to the benefits of logical concepts and critical thinking skills game programming could have immense benefits if built into the K-12 curriculum."

"This is a rather unusual structure for organizing mathematical content, but offers an exciting opportunity for teachers across the nation and abroad to exchange ideas and discuss what they teach. This Wiki will address the underlying central concepts and propose activities that also provide rich opportunity to engage students in the Mathematical Practices. "

Vocabulary or terminology building is a difficult task for many students. A variety of teaching techniques and strategies are needed to help them develop a true understanding related to concepts.

CK-12 Foundation's Basic Algebra, Volume 1 Of 2 FlexBook covers the following six chapters:Expressions, Equations, and Functions - covers the relationships among expressions, equations, and functions when variables are present. Also explored is how these ideas can be shown on graphs. Properties of Real Numbers - covers various forms that rational numbers can assume, including fractions, integers, and square roots. Also considered are different operations for manipulating rational numbers. Linear Equations - introduces students to methods of solving simple equations involving variables. Also covered are ratios, scale, and the percent equation. Graphing Linear Equations and Functions - provides students with a more in-depth understanding of equations by introducing coordinate plane graphing concepts such as intercepts and slope. Writing Linear Equations - focuses on writing various forms of equations based upon real-world data and already existing lines. Students will also learn about predicting data using a fitted line. Linear Inequalities and Absolute Value; An Introduction to Probability - covers operations of inequalities, including addition, subtraction, multiplication and division. These principles are then applied to absolute value and probability.

Parents who excel at maths produce children who excel at maths. This is according to a recently released University of Pittsburgh study, which shows a distinct transfer of math skills from parent to child. The study specifically explored intergenerational transmission-the concept of parental influence on an offspring's behaviour or psychology-in mathematic capabilities.

From the abstract (full text requires subscription or purchase): "Though cooperative learning has been a topic of considerable interest in educational research, there has been little study specific to learning in the mathematics content area of geometry. This paper seeks to address that gap through a design experiment featuring a novel small-group computing environment for supporting student learning about quadrilaterals. In this design, each student controls a unique point in a shared geometric space, and those points are linked such that a group of four students collectively forms a quadrilateral. We first present results from pre- and post-measures to show how the students learned from the activities and developed in terms of geometric reasoning. We then present three episodes, elaborated with the notion of appropriation, to explain how students took up ways of using the technological tools and of talking about geometric concepts from one another in the interactive environment. Our study found that students achieved learning gains in this novel environment, that the environment provided rich opportunities for peer interaction around geometric objects, and that student learning opportunities and interactions were characterized by processes of appropriating ways of talking about and using software features."

A slide show of artworks influenced by and demonstrating mathematical concepts