Evens and odds at f(t)
Kate usually works with older kids. Following comments from elementary school teachers, she became “a little obsessed” designing a lesson about proofs for young kids. Making deep concepts accessible is an exciting, challenging quest! The post starts with the video about proofs and creativity: what makes us different from computers. It has several visual, hands-on ideas that can introduce proofs to second or third graders. The activities start from students capturing their “noticings,” forming conjectures in Socratic dialogues, and eventually proving the conjecture that odd+odd=even.
Sasha first saw modeling of deep math with dolls at our place, Moebius Noodles. The first challenge Sasha designed for her daughter Katie was to alternate boy and girl dolls, in a story about a ball. With three of each, and six chairs in a line, Katie succeeded. Can you solve the same problem if one more boy arrives? Can you change the degree of all the vertexes in the graph to two, that is, help every doll to have two neighbors, while still alternating boys and girls? Grown-ups know that to change degrees of vertices, you need to change the shape of the graph, that is, to move the chairs into a new configuration. Can a little kid figure it out? Read on!
Robert is building on factorization diagrams, especially on work of Brent Yorgey and Sean Seefried. Factorization diagrams are so simple and intuitive! A few minutes with the game prototype Robert made will get children comfortable with the diagrams. The two calculators support exploration. The diagrams will appeal to kids who like visual arts, and the game mechanics will help to focus children’s attention. Robert plans to add scoring and badges, and to develop the game for iPad.
How children learn
Do girls have more anxiety than boys? – Asks the Stochastic Scientist
“Contrary to popular convention, girls don’t actually experience more anxiety than boys do during math tests or math classes. They just think they do.” Kathy opens with this surprising finding from a study of German schoolchildren by Thomas Goetz et al. The key differences between the sexes have to do with momentary vs. habitual math anxiety. Read on to see how the same momentary experiences cause different long-term consequences for boys and girls.
Steven looks at the model of life as a zero-sum of some variables, for example: A(career) + B(relationship) + C(finance) + D(character) = 0 - a plane in 4D space. By this model, people cannot be successful in all areas of life, but have to choose what areas of life are important. The assumption that the model resembles real life is not examined.
Sheryl blogs to help adults nurture their youngest children’s sense of wonder. For her, this journey began as a year-long project for Early Childhood Teacher Certification awarded by the American Mathematical Society. It is inspired by Montessori methods and Michael S. Schneider’s book A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science, A Voyage From 1 To 10. We need to be careful not to let simplicity escape us. Rather than only looking at the numbers 1-10 in the linear fashion, as we ordinarily do, SNAP is an invitation to observe various expressions of each number, individually, across all subject areas, using all of our senses. It is yet another way to support children as they practice careful discrimination, organize thought, and retrieve information in unique ways.
Maria shares her thoughts about Jo Boaler’s How to Learn Math course. “You see, all of our brains actually GROW and make new connections when we make mistakes and think about them. There is no brain growth if you can just sail through a problem set! That is why it is so important for our students to make mistakes — and then we need to VALUE those mistakes and help them learn from them.” Maria also talks about developing fluency through the number sense rather than timed tests.
Lilac from Learners in Bloom shares the list of math skills, such as parts of 3D shapes and arithmetic operations, and the corresponding games and activities for kindergarten. Her girls especially enjoyed building “mystery 3D figures” using clue cards that list the shapes of the faces. Lilac takes a list of skills from worksheets, but designs hands-on games and activities to achieve them. There are deeper mathematical bonuses than “just fun”: for example, all building tasks raise questions about different ways you can model the same concept.
Margo offers kindergarten kids a treat: a tactile enactment of addition. It is for the whole child: there’s whole body movement, use of manipulatives, some writing and creativity. Many public schools prohibit holiday parties. However, this party-ish educational activity can be done in the spirit of the holidays, without violating any rules.
Jeremy offers a homemade game, great in its versatility, to practice addition and subtraction. It can also lead to probability. Change the numbers on the die, use negative numbers if you want, change your target numbers… There are many possibilities for DIY fun!
Young children can learn all the math they need through games and activities, agree Julie and her friends. This method can be very motivating, especially when math has been a struggle in the past. Julie links specific games to arithmetic skills they teach. As a big bonus, games also teach strategic thinking, problem-solving, and other valuable mathematical practices.
This genre of puzzles gives kids one letter per exercise. The letters gradually assemble into a phrase. This procedure is a gamification device, that is, an engaging way to track progress and to manage your time and your tasks. Denise shares an exercise she remixed, since the original seemed like nagging. Traditionally, the phrases are funny or cute: they must be rewarding.
Do you model with physical or virtual objects? Why not both?! Christy invited her eight-year-old to explore positive and negative exponents, and some economics (less material for the same result) with Minecraft crafting tasks, and with plastic tiles. Why are stairs so expensive to make? Why can’t you split stacks into any number of empty inventory slots? Pet peeves in Minecraft lead to tasty math!
How do you improve your number sense? Here’s a list of objects, from tiny to huge. Can you put them in order by increasing size? Where is the biggest gap? How would you measure the gaps? Sue reviews activities and resources from other blogs, and offers her list of interesting, yet well-known objects to sort by size.
See how Fran and her kid used smileys and marine animals for tic-tac-toe? There is much math value in inviting kids to make these design decisions. It helps kids to see the essential elements of the game’s structure in general, abstract ways. In tic-tac-toe, the kid progresses from Xs and Os (a particular case) to two different types of markers (the abstraction). Fran thinks strategy games are a great way to build critical thinking and decision-making skills, as she educates her kid at home. They had a great time making and playing on their own game boards, and thought others would too!
Tom shares full materials for one of the major labs he designed for his Algebra I class. The simple visual sparks interest at a very low entry cost: any student can vote which of the three pictures represents the area where it is cheaper to drive than to fly. Plus, it’s a real life dilemma for anyone who travels regularly! The lab uses spreadsheet tools, such as lines of best fit.
What do math teachers do on vacation? Hint: it involves chalk, a bucket of water, a tennis ball, and math graffiti! Lucy writes: “My kids thought this activity was so much fun! And now my 2nd grader and 5th grader understand the coordinate system.”