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Pattern blocks are great tools for developing conceptual understanding. I hope to continue to see them used in classrooms, but the virtual kind can allow students to share their thinking with other students virtually. I like using screen capture, cut/paste, upload to a wiki, comment on characteristics/size/description of '1'/and sharing with students so that their thikning can be revisited from multiple venues (home, classroom, internet-broader audience).

A Dustbin game is great for helping students to organise ideas into categories. Students or teachers can create up to four categories of factors. The game created by ClassTools.net then involves students dragging and dropping each factor into its correct category as quickly as possible in a "race against the clock"!

Dustbin Game template and ideas. Great idea for organizing information.

Active learning has a powerful impact on student learning. How? Student achievement increases through mastery of science and math content as a result of this technique. Students also develop improved problem solving, communication, and higher order thinking skills.

"This paper describes a research project on Year 3 primary school students in Malaysia in their use of computer-based video game to enhance learning of multiplication facts (tables) in the Mathematics subject. This study attempts to investigate whether video games could actually contribute to positive effect on children's learning or otherwise. In conducting this study, the researchers assume a neutral stand in the investigation as an unbiased outcome of the study would render reliable response to the impact of video games in education which would contribute to the literature of technology-based education as well as impact to the pedagogical aspect of formal education. In order to conduct the study, a subject (Mathematics) with a specific topic area in the subject (multiplication facts) is chosen. The study adopts a causal-comparative research to investigate the impact of the inclusion of a computer-based video game designed to teach multiplication facts to primary level students. Sample size is 100 students divided into two i.e., A: conventional group and B conventional group aided by video games. The conventional group (A) would be taught multiplication facts (timetables) and skills conventionally. The other group (B) underwent the same lessons but with supplementary activity: a computer-based video game on multiplication which is called Timez-Attack. Analysis of marks accrued from pre-test will be compared to post- test using comparisons of means, t tests, and ANOVA tests to investigate the impact of computer games as an added learning activity. The findings revealed that video games as a supplementary activity to classroom learning brings significant and positive effect on students' retention and mastery of multiplication tables as compared to students who rely only upon formal classroom instructions."

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."

Abstract: "Students' attitudes toward mathematics and its learning have been subject to numerous studies in the past six decades. These studies treat such attitudes as both desirable learning outcomes and correlates of mathematics achievement. Many Likert-type attitude scales have been devised to measure significant constructs underlying mathematics-related attitudes, such as confidence, anxiety, and utility of mathematics. The psychometric properties of these attitude scales may be culture and age dependent. As part of a research project called Singapore Mathematics Assessment and Pedagogy Project (SMAPP), an effort was made to devise and validate an attitude toward learning mathematics scale that can be used with lower secondary school students in Singapore. This paper explains the use of exploratory and confirmatory factor analyses to reduce an initial 57-item questionnaire to one with 24 items that cover these six dimensions: Checking solutions, Confidence, Enjoyment, Use of IT in mathematics learning, Multiple solutions, and Usefulness of mathematics. The data comprise responses from about 890 Secondary 1 (Grade 7) students in 2010, who took the 57-item questionnaire, and another 850 students who took the 24-item questionnaire in 2011. The nature of the final questionnaire is discussed. This effort contributes to the continual effort to devise validated attitude scales that are suitable for different cultures and student groups."

" 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)

Flipping a classroom is not a teaching technique, it is more in line with a philosophy or way of teaching. It involves using technology as a tool, not the main focus, for helping students increase their understanding of science or math concepts.

Your students' future and education needs are not like yours and mine. For the most part, we are a product of an education system heavily influenced by the industrial age - lectures and rote memorization. This style of teaching was primarily designed to produce factory and skilled trade workers.

From the abstract: "The problem addressed by this study is the need to identify practical predictors of success for community college developmental mathematics students in online, hybrid and seated course delivery formats. This study examined two possible predictors of success, mathematics self-efficacy and technology self-efficacy, in the three delivery formats and how they related to performance on a final assessment. The study used a quantitative research design employing binomial logistic regression to determine if the independent variables (math self-efficacy and technology self-efficacy) were significant in predicting the outcome category (score on the final assessment dichotomized about the mean). Next linear regression analysis was used to build a predictor equation for a particular score on the outcome variable. A previously developed survey and an adapted version of another survey were combined to measure the independent variables; demographic factors were also measured for descriptive purposes. Binomial logistic regression analysis showed that math self-efficacy was a valid predictor of success for the developmental math students in this study but technology self-efficacy was not. Regression analysis produced a valid equation to predict standard score from average math selfefficacy score. When separated into groups according to course format, math self-efficacy was only a valid predictor for students in hybrid courses. The implications of these results are discussed and recommendations are made for further research."

Huge collection of math resources for any level student or teacher.

Let's give students learning tasks that tell them, "You can be as smart as you want to be." Great article on changing the mindset of American mathematics students from smart kid.s are smart rather than smart kids work hard to be smart. 

Profiles a study by the Rand Corporation that contradicts other studies and reports by showing that student test scores in math and science have not declined over the last decade. Whether there is a correlation between student performance and technological growth remains to be seen.

My name is Patrick Honner. I teach mathematics at Brooklyn Technical High School, a large, public, specialized high school in Brooklyn, New York. As a NYC public school teacher I have taught everything from Introductory Algebra to Multivariable Calculus.  I mentor student research in mathematics, and I am actively involved in extracurricular mathematics programs both in my school and around New York City. Math research is an instructional focus of mine. Independent, investigative, mathematical research projects can be crafted by and for students at all levels of knowledge, in all areas of interest. A primary objective of MrHonner.com is to exhibit the math all around us in order to stimulate question-posing and hypothesizing, the first steps in structuring a good research project. I am a two-time recipient of Math For America's Master Teacher Fellowship, and I am active in MfA's professional community.

"SRI International, Worcester Polytechnic Institute (WPI), and the University of Maine have received a $3.5 million award from the Institute of Education Sciences at the U.S. Department of Education to evaluate the effectiveness of an online tutoring system for mathematics homework. The research team will study seventh-grade mathematics students and teachers in more than 50 schools throughout Maine using WPI's ASSISTments system. ASSISTments aims to transform homework by giving students instant feedback and tutoring adapted to their individual needs. It also provides teachers with customized reports each morning on their students' nightly progress. Teachers in the study will receive training in how to use these reports to adapt their lesson plans to better suit students' needs."

Electronic tutoring system, to help students with standardized tests gauges students' responses as they learn, received a ONR grant http://www.umass.edu/newsoffice/newsreleases/articles/148281.php

Abstract: Educational videogames can be designed to provide instructional feedback that is responsive to specific actions. However, existing research indicates that students tend to ignore videogame feedback and subsequently use less effective help-seeking strategies. Research on help-seeking in learning environments has primarily focused on the role of cognitive factors, the nature of the help, or issues of timing and frequency. There is a noticeable gap in understanding regarding how to motivate and increase the use of feedback for improved learning. Using a pre-algebra videogame, this study examined the relationship between an incentive to use feedback and math achievement. A randomized-control design was employed, which compared learning outcomes of students who received the incentive to those who did not. Results indicated that students given the incentive to use feedback had significantly higher normalized change scores on math items (d = .53), with stronger effects for students with low academic intrinsic motivation (d = .88 - 1.17).

There are plenty of calculator apps in Google Play, but IDEAL WebMath is different because it shows students how to solve a problem.  IDEAL WebMath can help students with addition, subtraction, multiplication, division, comparing fractions, ratios, proportions, place values, and rounding.

This practice guide provides five recommendations for improving students' mathematical problem solving in grades 4 through 8. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students.