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From the abstract (full text requires subscription): "Many organisms can predict future events from the statistics of past experience, but humans also excel at making predictions by pure reasoning: integrating multiple sources of information, guided by abstract knowledge, to form rational expectations about novel situations, never directly experienced. Here, we show that this reasoning is surprisingly rich, powerful, and coherent even in preverbal infants. When 12-month-old infants view complex displays of multiple moving objects, they form time-varying expectations about future events that are a systematic and rational function of several stimulus variables. Infants' looking times are consistent with a Bayesian ideal observer embodying abstract principles of object motion. The model explains infants' statistical expectations and classic qualitative findings about object cognition in younger babies, not originally viewed as probabilistic inferences."

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."

Abstract:"This paper discusses the results of a pilot st udy that explored how prospective secondary school teachers are shaped by learni ng experiences during their undergraduate mathematics education. The collabora tive study, which was conducted by a mathematician and a mathematics educator, dr ew from the experiences of prospective teachers in a non-traditional undergraduate ma thematics program that makes extensive use of technology. Analysis of data collect ed from detailed questionnaires, journals, and focus group discussions strongly suggests that designing, implementing, and testing Learning Objects promotes prospective teache rs' learning of the mathematics needed for teaching. Furthermore, the analysis shows t hat prospective teachers' experiences of ownership, engagement, and pride are key to positive learning experiences. "

In this lesson, students learn how to measure the area of the tire footprint on a car and to find air pressure using a tire gauge. Students then find the weight of the car using their fraction multiplication skills. Learning Objectives   Students will: Estimate weight of a large object Use a ruler and a tire gauge to take measurements Collect and record data Review square units of measure Calculate area by multiplying fractions Materials   Strips of poster board Ruler Tire gauge How Much Does a Car Weigh? Activity Sheet Computer with internet connection Car Instructional Plan In preparation for this lesson, place a car in a safe lcation for the students to measure the tire footprints and pressure. In case of bad weather, find a covered location. Be sure to measure the tire footprint and the pressure (in PSI) of each tire ahead of time, so that you will be able check the accuracy of students' measurements. Also, check the accuracy of your calculation by comparing to it to the weight of the car listed on the sticker inside the driver's door or in the vehicle manual. By the end of the day, data may change because air has leaked out of the tires while students were using the tire gauge. For safety, check the tires before driving home.

from the article: "it's algebra, the academic subject that more than any other strikes fear in grown-ups' hearts. But these are 5th graders. And some are struggling learners. The lesson is plenty rigorous, as you'll see. But the kids get a useful assist from the "manipulatives," concrete objects -- pawns and blocks -- that support a program called Hands-on Equations. Kids use the objects to build and break down algebraic equations."

The main objective of the Intergeo Project is to make digital content for mathematics teaching in Europe more accessible, usable and exploitable. Intergeo will... * offer content in a searchable and metadata-tagged portal. * enable users to use their software of choice by specifying a common file format based on open standards. * test available material in the classroom. All stakeholders, software teams, resource authors, teachers and learners will be involved, in order to promote quality enhancement cycles.

The main objective of the Intergeo Project is to make digital content for mathematics teaching in Europe more accessible, usable and exploitable. Intergeo will... * offer content in a searchable and metadata-tagged portal. * enable users to use their software of choice by specifying a common file format based on open standards. * test available material in the classroom. All stakeholders, software teams, resource authors, teachers and learners will be involved, in order to promote quality enhancement cycles.

Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "

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The objective of this site is to show examples of thinking in math, whether it is original solutions from students of problems, or ways to include an inquiry based approach in mathematics education. The idea for the project came from Chris Hunter as a comment on a blog post. I, David Wees, think it is such a terrific idea that I am working on implementing it. I welcome ideas and input from anyone who is interested and would like to help support student thinking in mathematics. Please send an email with your example of original mathematical thinking by a student, or an example of a project students can do to support inquiry in mathematics

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.

A site with a collection of maths videos designed to get students drawing graphs. Watch the motion of objects or values on scale in the videos and plot the numbers. The videos have the correct answers at the end.

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 well made Mandarin resource for kids. Choose a topic page then hover over the objects to see the characters and pinyin and hear the pronunciation. http://ictmagic.wikispaces.com/Mandarin+%26+Chinese+culture

discalculia.pdf (application/pdf Object)

" 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)

Description of a University of Queensland study involving 36 infants, half 15 months and half 18 months. Tests with counting videos suggests that the 18 month old children have a grasp of counting rules before they can count (for example, understanding that objects can be counted only once." Further research using brain imaging is suggested.

Thanks - this will be useful for my "Math-rich baby" online class!

Matching pairs game http://bit.ly/ewGe9 more levels than you can shake a stick at

Free resources for teaching maths using primary framework objectives

Using the equation editor that comes with Microsoft Word, equations can be inserted into Word, PowerPoint, or any application that supports OLE (Object Linking and Embedding). Although most of this document provides instructions pertaining to Word, the procedures for inserting and editing equations in Word are the same as for PowerPoint. Some PowerPoint specific notes can be found at the end of this document.

Demonstrates the utility of exergames for teaching and learning. "Our goal is to design a math game for children aged between 8 and 12. Our focus in basic operations: adding, subtracting, dividing and multiplying. Players must gather a given number of objects in order to properly complete mathematical operations while at the same time avoiding or destroying other objects that cause him to lose energy or reduce the time given to complete the task."

"Research has been conducted on how to aid blind peoples' perceptions and cognition of scientific data and, specifically, on how to strengthen their background in mathematics as a means of accomplishing this goal. In search of alternate modes to vision, researchers and practitioners have studied the opportunities of haptics alone and in combination with other modes, such as audio."