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Writing in math is an excellent way to determine if students' understand or do not understand the math they are learning about. Allowing students to explain how they solved a math problem, how they developed a formula to solve a problem, or how they applied a math concept requires critical thinking.

LOGIN Wednesday February 15 at 3pm Eastern US time: http://tinyurl.com/math20event During the event, Dr. Keith Still of SaferCrowds.com will introduce his Crowd Sciences work and explain the relevance of mathematics in it: "If you don't do the maths, you could end up in court on a manslaughter charge!" All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at http://mathfuture.wikispaces.com/CrowdSciences Pose questions and comments for Keith before the event Math Future wiki: http://mathfuture.wikispaces.com/message/list/CrowdSciences LinkedIn group: http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=94871153&qid=b29a6dbc-6474-425f-865a-b319bd33dcb9 Email group: http://groups.google.com/group/mathfuture/browse_thread/thread/931328aab6d87b03 How to join Follow this link at the time of the event: http://tinyurl.com/math20event Wednesday, February 15 2012 we will meet online at noon Pacific, 3 pm Eastern time. WorldClock for your time zone. Click "OK" and "Accept" several times as your browser installs the software. When you see Session Log-In, enter your name and click the "Login" button If this is your first time, come a few minutes earlier to check out the technology. Crowd Modelling + Crowd Monitoring + Crowd Management = Safer Crowds Crowd Modelling is the scientific approach to the development of safe, robust, crowd management plans. This can be achieved without the need for expensive, complex, time consuming computer simulations. In simple terms Crowd Modelling is understanding how, where, when and why crowds arrive, move around and leave an events/venues. The majority of this can be accomplished using tried, tested and simple to apply methodologies. "Keith Still is what I term an intuitive mathematician. He is one of the most creative and original thinkers that I know. He adds drive and determination, as well as considerable intellectual power to any group of which h

" 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.

Nice set of applets that let students explore fraction understanding from multiple perspectives and models. I love that they use a variety of models for fractional development, including bars (multiple versions), sets, and linear. From the site:  "Why Fractions? Fractions are one of the earliest stumbling blocks for students in math. Our goal is building conceptual understanding in fractions as a basis for comprehension in all later topics."

An algebra project focusing on a theme which interests students is more likely to engage them in the project, so lets take a look at sports. Many students participate in sports at some level, whether as part of a school team or a community team. For the most part these same students do not understand the costs involved to host the sport. Also, they do not understand how much money is needed to ensure a profitable season so the sport can continue from year to year.

The Final Report of the National Mathematics Advisory Panel noted that many middle school students have a weak understanding of mathematical equality and that this lack of understanding impedes their learning of algebra.

Alternative assessments provide you opportunities to determine the true level of understanding your students have regarding science and math concepts. These tools improve the learning environment for your students, along with your assessment of their real understanding.

"A researcher's journey towards increased understanding of his field"

Understanding math through music.

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.

by dr. sarah-marie belcastro, "You might wonder why one would want to knit mathematical objects. One reason is that the finished objects make good teaching aids; a knitted object is flexible and can be physically manipulated, unlike beautiful and mathematically perfect computer graphics. And the process itself offers insights: In creating an object anew, not following someone else's pattern, there is deep understanding to be gained. To craft a physical instantiation of an abstraction, one must understand the abstraction's structure well enough to decide which properties to highlight. Such decisions are a crucial part of the design process, but for the specifics to make sense, we must first consider knitting geometrically."

"In previous posts, I have summed up my position on Khan Academy as follows: Khan Academy teaches only one part of mathematics-procedures-and that isn't the most important part. Writing about mathematics, developing a disposition for mathematical thinking, demonstrating a conceptual understanding of mathematical topics are all more important than procedures. That said, procedures are still important, and Khan Academy provides one venue where students can learn them. In the end, I think every young person should have an account there. Even if only one in a thousand or ten thousand benefit, that would be a terrific outcome. "

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.

Help your students understand equivalence between fractions, decimals and percentages with this visual number line flash resource. Peg the value to the correct position. http://ictmagic.wikispaces.com/Maths

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.

"Primary school students are more likely to understand and engage with maths if classes use real money and real-life projects, according to a Western Sydney University pilot study. The findings come as Australian students lag behind other countries in maths, with Year 4 students dropping from 18th to 28th out of 49 countries in year 4 maths in the latest Trends in International Mathematics and Science study."

"Italian psychologist Geatano Kanizsa first described this optical illusion in 1955 as a subjective or illusory contour illusion. The study of such optical illusions has led to an understanding of how the brain and eyes perceive optical information and has been used considerably by artists and designers alike. They show the power of human imagination in filling in the gaps to make implied constructions in our own minds. Kanizsa figures and similar illusions are a really useful way to encourage learners to 'say what they see' and to explain how they see it. It offers a chance for others to become aware of the different views available in a diagram and share their own thoughts without the 'danger' of being wrong; many people see different things."

"The MIND Research Institute enables elementary and secondary students to reach their full academic and career potential through developing and deploying math instructional software and systems. A non-profit organization, MIND also conducts basic neuroscientific, mathematics, and education research to improve math education and advance scientific understanding."

Current reforms in mathematics education emphasise the need for pedagogy because it offers learners opportunities to develop their proficiency with complex high-level cognitive processes. One has always associated the ability to make mathematical connections, together with the teacher's role in teaching them, with deep mathematical understanding. This article examines the nature and quality of the mathematical connections that the teachers' representations of those connections enabled or constrained. The researchers made video recordings of four Grade 11 teachers as they taught a series of five lessons on algebra-related topics. The results showed that the teachers' representations of mathematical connections were either faulty or superficial in most cases. It compromised the learners' opportunities for making meaningful mathematical connections. The researchers concluded by suggesting that helping teachers to build their representation repertoires could increase the effectiveness of their instructional practices.