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"Below is a set of good iPad apps that you can use with your kids and students to enhance their mathematical thinking. These apps are meant for young learners and are specifically useful when introducing kids to those rudimentary notions of mathematical computations. The purpose of teaching kids to think mathematically, as detailed in Kaye Stacey's paper, is three folds: First, it will allow kids to conduct mathematical investigations by themselves. Second, it will help them acquire other thinking skills particularly problem-solving and as mathematician Paul Halmos (1980) stated, 'problem solving is the heart of mathematics'. Third, it helps kids get a deeper appreciation of mathematics and use it in their daily and working lives."

"We have designed a Mathematical Mindset Guide to help teachers create or strengthen a growth mindset culture. This guide contains five Mathematical Mindset Practices along with links to teaching videos.  The videos all show Jo and Cathy teaching middle school students. There are different stages described in each practice to help capture the journey of a mathematical mindset classroom and the evidence teachers may collect along the way for their own reflection or for discussion with colleagues.  The guide has been designed for teachers to use in the process of self-reflection, or for coaches or administrators to use to encourage a mindset teaching culture. In the interactive version of the guide on this web page, you can click on the arrow buttons in the Expanding descriptors to see a short extract of Jo/Cathy teaching in the ways described. Our goal for the guide is to support a mathematical mindset journey of learning and growth. Teachers can work with the guide individually or in collaboration with others. The guide is intended to be non-judgmental, non-evaluative, and iterative in nature. When using the guide consider the classroom community as a whole rather than the teacher alone. It is also important to note that while the goal of the guide is to communicate all aspects of a mathematical mindset classroom, it is not always possible to find evidence of all practices in one lesson. We encourage teachers, coaches, and administrators to use this guide, and our reflection suggestions iteratively over multiple lessons."

The goal of Natural Math is to collect, distribute and create such natural experiences of mathematics. We need to work with families to support them as units of larger communities of practice. We need to participate and engage babies and kids in math-rich, meaningful human endeavors that are useful, beautiful and fun. From the earliest time, kids should see themselves as co-creators of mathematics. Finally, the richness of the mathematical culture has to become available and accessible, beyond ivory towers of specialists and lairs of geeks "The future is here. It's just not evenly distributed." All the pieces of the natural math puzzle already exist in various "math oases" where families, subcultures, online communities and other groups of people engage with mathematics in ways that are natural for humans. We can put the puzzle together by networking: identifying activities that support natural math, supporting families and communities in finding and developing such activities, and loving one another in the context of mathematics.

"One snowy January day, I asked a classroom of college students to tell me the first word that came to mind when they thought about mathematics. The top two words were "calculation" and "equation." When I asked a room of professional mathematicians the same question, neither of those words were mentioned; instead, they offered phrases like "critical thinking" and "problem-solving." This is unfortunately common. What professional mathematicians think of as mathematics is entirely different from what the general population thinks of as mathematics. When so many describe mathematics as synonymous with calculation, it's no wonder we hear "I hate math" so often. So I set out to solve this problem in a somewhat unconventional way. I decided to offer a class called "The Mathematics of Knitting" at my institution, Carthage College. In it, I chose to eliminate pencil, paper, calculator (gasp) and textbook from the classroom completely. Instead, we talked, used our hands, drew pictures and played with everything from beach balls to measuring tapes. For homework, we reflected by blogging. And of course, we knit."

"Math has been a traditionally thorny subject in many American schools. Lots of children dislike math and many more adults stopped taking mathematics as soon as they are able, even when they were successful in their classes. At the same time, mathematical thinking is a crucial part of many of the most exciting and growing careers in science, technology, engineering and math, not to mention important for a general understanding of the mathematical world around us. So, what can U.S. math educators do to shift this dynamic? Stanford Mathematics Education Professor Jo Boaler is championing a dramatic shift in how many math teachers approach instruction. Rather than focusing on the algorithms and procedures that make mathematics feel like a lock-step process -- with one right way of solving problems -- Boaler encourages teachers to embrace the visual aspects of math. She encourages teachers to ask students to grapple with open-ended problems, to share ideas and to see math as a creative endeavor. She works with students every summer and says that when students are in a math environment that doesn't focus on performance, speed, procedures, and right and wrong answers they thrive. They even begin to change their perceptions of whether they can or can't do math."

"It is common for people to group themselves into two categories; those who are good at art or design, and those who are good at math or science. The reason for this is that many people believe that the skills needed to be successful in creative services do not relate to the skills that are required to be successful in the analytical. Even though mathematics is in the list of the most difficult college classes, in reality, nothing could be further from the truth. Many design concepts, such as symmetry, have direct ties to mathematical concepts and discoveries. So, if you are an artist or a designer, there is a good chance that you are already incorporating math into your work, you just may not be doing it consciously. Here are some very specific ways that mathematics has not only influenced design but has acted as a true game changer."

"This week I'd like to talk about a topic that has been a focus in my role as an Instructional Coach this past year - that of mathematical thinking, reasoning and proving. I supported teachers in my schools in these areas and it has been great to see students develop and demonstrate their mathematical thinking, aligned with learning goals and success criteria. When students reason and prove in mathematics, they are explaining their thinking and providing the evidence in a systematic manner using a variety of representations. Many times, it is difficult to understand what a student is showing in his/her work. Before I provide some suggestions, we need to understand what reasoning actually is; what is reasoning?"

"I learned about the math kits from the book, Reggio-Inspired Mathematics and grateful for the power of Twitter and the opportunity to directly connect with Janice. I asked and she kindly sent the list of materials for each kit. I will be putting together a set of math kits and sharing with my students the three formats for mathematical provocations. As described by Gandini (1998) provocation is something arriving by surprise. Provocation is a means for provoking further action. I like that the book links provocations and invitations as one in the same responding to the question about "what's the difference" that I hear so often. Let's get beyond trying to define them so discreetly and get onto the task of creating them in multiple formats. "

"Benefits of Coding At the heart of computational thinking - and mathematics - is abstraction. When children write code, they come to… understand in a tangible way the abstractions that lie at the heart of  mathematics, dynamically model mathematics concepts and relationships, gain confidence in their own ability and agency as mathematics learners. Computer coding is creating a buzz in education. Prime Minister Justin Trudeau recently said, "We need to do a lot better job of getting young people to understand what coding is and how it's important, how to program, how to problem solve, how to create the most elegant algorithm possible."1 BC recently announced that computer coding will be added to all grades of the K-12 curriculum, and Nova Scotia has made a similar announcement. The trend of adding some form of computer coding to curriculum is an international phenomenon; in 2014, England mandated a coding curriculum for all K-12 students."

The landing of the Perseverance rover on Mars is an excellent catalyst for a discussion with students about the nature of Mathematics. It is a chance to inspire curiosity and wonderment and to do so through a mathematical lens.

"It's often easy to get stuck into a narrow view of what a particular field of study entails, but as Dominic Walliman reveals in his impressive science infographics, there's much more than meets the eye when thinking of particular STEM subjects. Walliman demonstrates the diversity and complexity of biology, chemistry, computer science, physics, and mathematics in visual maps that explore the breadth of each field. Walliman, who also created animated videos exploring his science infographics, manages to pack all the shades of each complex field on one page. For instance, the Map of Mathematics travels from the origins and foundations of the field to the differences between pure mathematics and applied mathematics. Likewise, chemistry is divided between rules and different sub-topics like biochemistry and inorganic chemistry, with fun illustrations to clearly show what falls underneath each area. Whether you are a scientist who feels like people never quite get what you do or a student who can't put their finger on how they might use their math or science degree, Walliman's infographics will come in handy. Consider them roadmaps to possible careers or cheat sheets to figuring out how quantum physics is related to the theory of relativity. Best of all, by studying the visual maps, it becomes easy to see how all these scientific fields overlap and fit together like a puzzle."

"Many people find mathematics daunting. If true, this piece is for you. If not, this piece is still for you. What do you think of when you think about mathematics? Perhaps you think about x's and y's, intractable fractions, or nonsensical word problems. The cartoonist Gary Larson once depicted hell's library as containing only giant tomes of word problems. You know, "If a train leaves New York…" I was trained as a mathematician, and I will let you in on a trade secret: That is not what mathematics is, nor where it lives. It's true that learning mathematics often involves solving problems, but it should focus on the joy of solving puzzles, rather than memorizing rules. I invite you to see yourself as a problem solver and mathematician. And I'd like to introduce you to the man who once invited me to the study of problem solving: George Pólya."

"Today, declining mathematics scores is a new challenge that will not wait. In elementary schools across Ontario, educators are responding. Reflected here are the stories of some schools that have seen their mathematics scores move from below the provincial target five years ago, to meeting or exceeding the target five years later."

"The students in Molly James's kindergarten classroom were tasked with creating a mathematical art gallery. They had each drawn a number and then searched for two types objects they could use to compose a visual number sentence - such as two rulers plus three scissors to equal five objects. After photographing and mounting their pictures on the wall in numerical order, the students sat on the floor with their sketchbooks and began to draw and talk. "I had expected them to learn something about number composition," James said, "but I didn't expect the remarkable observations they began to have about the photographs." For example, when one girl looked at a picture of two red scissors and three blue scissors (2+3=5), she noticed that the direction of the handles gave rise to a new number sentence: 4 scissors pointing left + 1 scissor pointing right = 5 scissors. James, who recently published a paper about creativity in the classroom, said moments like these remind her that "creativity is not fluff or an add-on, but is instead an essential part of what it means to be a mathematician."  In fact, she believes creativity is the key to helping her students become confident and skilled mathematical thinkers."

"Math has been a traditionally thorny subject in many American schools. Lots of children dislike math and many more adults stopped taking mathematics as soon as they are able, even when they were successful in their classes. At the same time, mathematical thinking is a crucial part of many of the most exciting and growing careers in science, technology, engineering and math, not to mention important for a general understanding of the mathematical world around us. So, what can U.S. math educators do to shift this dynamic?"

"Below is a collection of some of the best iPad math games for young learners. These apps involve strategic use of mathematical skills in working on simulated challenges. While an entertaining source of fun, these games are also ideal for providing kids with a solid math practice to enhance their overall mathematical thinking. Check them out and share with your students."

We provide ideas and resources for use in secondary mathematics on interactive whiteboards. Link directly to over 500 mathematics interactive web pages from our subscription site. Read the What's new section. Take out a subscription (for £50). See what we come up with for free daily (page of the day, mathematician), weekly (curve, polyhedron, triangle) and monthly (MEI, Movie) all on one site.

Reading and Writing Mathematics

Reading and Writing Mathematics

Reading and Writing Mathematics

"Welcome to the ORC Stella website. The core of this collection is a library of more than 600 non-routine mathematics problems known as Stella's Stunners to be launched set by set over the coming months. The problems range from simple visual problems, requiring no specific mathematical background, to problems that use the content of Pre-Algebra, Algebra I, Geometry, Algebra II and Trigonometry, up through Pre-Calculus. The Stella problems are not typical textbook exercises. They are considered "non-routine" problems because the methods of attacking them are not immediately obvious. Because these problems can supplement and enliven traditional mathematics courses in a variety of ways, we have included materials to assist in using Stella problems in your teaching: "

"For too many students, doing mathematics means just plugging numbers into a memorized formula to get an answer. And because they don't understand the formulas they're using, they often fail to use the right one. Take a look at Isaac's work below, for example. He is a fifth grade student who tried to find the surface area of a rectangular prism by incorrectly adapting a previously memorized formula for calculating perimeter. He calculated two times the length plus two times the width (2L + 2W) and tried to account for the height by multiplying it by 4, then adding it to the previous sum. Unfortunately, Isaac is not alone in this type of approach. Students who use formulas by rote may never come to see mathematics as sense-making and may never understand the formulas they use. And there are so many formulas to memorize! Teachers who prematurely introduce students to formulas risk denying them opportunities to develop the necessary conceptual foundations for mathematical understanding."