Ah, summer. For kids, it’s the greatest time of year. No school, no multiplication tables, no scheduled break times. Just long, happy days in the sun. But what happens to children’s brains during that time of relaxation and fun? It’s a fact of life – during the summer months, young students will lose a certain amount of the information they have learnt during the school year. The exact loss is approximately two months’ worth of reading and mathematical skills, referred to as ‘summer learning loss’ or ‘brain drain.’ The gap in consistent education caused by the summer break may be yearned for by the students – those long summer days with no school are what dreams are made of – but it has an undeniable impact on the abilities of the children to retain the crucial information they learnt in the classroom. Math loss is the most significant, and it’s easy to see why. Children can still be stimulated intellectually whilst on holiday: reading, museums, trips to the zoo, and other cultural activities will continue to enhance and complement the skills and knowledge learnt at school. However, it’s unlikely that these trips will be contributing to their knowledge of fractions and long division. Math gets neglected, not because it doesn’t exist, but because it’s harder to think of math as existing outside of the classroom. So what can be done to counteract this? There are, in fact, lots of ways to create and continue math-learning situations outside of school. They don’t have to be dull, or less engaging than other activities – they can easily be incorporated into the... read more

I was recently asked to bring a cake to a reception on very short notice. Luckily, I found this recipe for Olive Oil Cake by Marcella Hazan, for which I had all the ingredients. I had two small lemons left in the fridge, and I conveniently assumed that the zest of both of them will be equivalent to the “zest of one lemon” required by the recipe. Was I right? Just out of curiosity, I asked myself: What would be the size of the hypothetical one lemon which would yield the same amount of zest as my two small lemons? Would this be a gargantuan lemon of mythical size, or just a regular looking fruit? This was easy enough to determine, since my two small lemons were nearly spherical, with diameter of about 2 inches: The lemon zest layer is so thin, that its amount can be measured by the surface area of the lemon times its thickness. Using the formula for the surface area of a sphere of radius r, Surface Area =4πr², and the fact that our lemons have a radius of about an inch, we have that the surface area of each lemon is about 4π square inches. So the surface area of the two small lemons is 8π square inches. How large a single lemon would have to be in order to have surface area of 8π square inches? Its radius, R, is given by this equation: 8π = 4πR² So R=√2≈1.4 inches. That’s not that big! At just 2.8 inches diameter, this hypothetical lemon would be well inside the range of lemons supplied by Sunkist growers. So it was a good call to replace... read more

“Geometry will draw the soul toward truth and create the spirit of philosophy.”—Plato. There is a widening gap between the effective teaching of geometry in elementary schools and the geometry skills students need in high school. Often, geometry tasks at the younger grades are limited to identifying shapes or labeling properties; in high school, students are expected to use abstract reasoning to prove a complex relationship. Dynamic, engaging instruction in geometry has traditionally been overlooked during middle school, causing a critical gap between elementary school experiences and the thought processes required in high school. Why do we need geometry in schools? Geometry is all around us. It is part of our daily lives, whether we are at a cafe (see picture below), a construction site, or at the post office. Geometry gives us the tools to engage analytically with our everyday surroundings. It turns out that these tools provide us with more than just an amusing intellectual exercise. A growing body of research links spatial reasoning with future success in other academic pursuits. Interestingly, these pursuits reach far beyond geometry or even mathematics. Elementary school teachers and researchers at the University of Toronto found that students given lots of spatial reasoning exercises ended up doing better in numeracy, patterning and other areas of mathematics. In an unrelated study, researchers showed that spatial thinking skills are strongly related to students’ future success in STEM disciplines. A common notion held by many people is that math is mostly about numbers. This erroneous idea is part of the reason that many people write themselves off as being “not good in math”. Not only... read more

Last week the first ever Julia Robinson Mathematics Festival was held in San Diego. What a great event celebrating the joy of math in a non-competitive atmosphere. About 70 students, mostly from grades 6-8, were in attendance. My favorite part was watching kids be comfortable enough to admit what they don’t remember, and figure it out right there. It was also great to see kids (and adults!) get really silly with math. Activities included a engaging recreational problems from many different areas of mathematics. You can see them in the San Diego Union Tribune gallery. We were honored to host a table with Geometiles.... read more

If you are going to coach a math club, it is likely that you will come across at least some of the following challenges: A classroom full of students at different levels, despite the fact that most students in the math club self-selected to be there Creating an atmosphere where students feel emotionally safe enough to participate in the class– meaning to risk providing wrong answers Assessing your students’ understanding, other than by testing The three challenges are interrelated, and I will describe some ways of addressing them. Most of the ideas are gathered from other successful teachers and were chosen because the issues they address echoed my experiences in Math Club. Students at different levels This is obviously a loaded subject, and I’d like to focus just on the interpersonal dynamics of a class in which students are performing at different levels. Let’s be honest: math clubs tend to attract high performing students, and, in my experience, such students often have a strong desire to demonstrate to everyone else just how high performing they are. If you are starting a math club, you need to be attuned to this from the very beginning. Otherwise, some serious damage can be done to the learning experience of your students who are either not as high performing, or less confident. My personal suggestion is to nip in the bud any behavior that smacks of arrogance. Do not wait until the damage is done. If there is one phrase that I could eliminate from any math club discussion, it would be “This is easy”. This phrase, and its consequences, are addressed in an article by Tracy Zager, a well-known math teacher... read more

Here are some of our blogs about Platonic and Archimedean solids: Public art installation in Los Angeles featuring huge Platonic and Archimedean Solids Examples of Platonic Solids in antiquity More lesson plans... read more