Tile Farm and the NCTM Process Standards

At Tile Farm, the National Council of Teachers of Mathematics (NCTM) Process Standards are always at the forefront of our minds when we create new content.  Published in the year 2000, the NCTM process standards outline essential components of a high quality math education that are applicable to learners of any age.  Our favorite thing about the NCTM Process Standards is that they are not only great for math education, but their concepts extend far beyond math learning.  Problem solving, communication, proof and reasoning, representations, and seeing connections permeate through all walks of life.  Thus by making a curriculum inspired by the NCTM Process Standards, we are not just training students for success in math education, but to be confident and creative thinkers in an ever changing world.  In this blog post, we explore five Tile Farm activities that highlight our alignment with the five NCTM Process Standards.

Problem Solving in Tile Farm Academy’s Big Thinker Puzzles

Tile Farm Academy’s Big Thinker is a set of weekly puzzles all about training students to become persistent , patient, and confident problem solvers.  These puzzles are meant to push students beyond their comfort zone, teaching them that struggling and making mistakes are an integral part of problem solving, and essential to their growth as a learner.  With unique sets of puzzles every week, students develop cognitive flexibility as they apply their problems solving skills in a wide variety of contexts.  This ultimately paves the path for students to become perseverant problem solvers in all walks of life as they continue to grow as human beings. 

In Big Thinker: Shape It puzzles, students gradually develop their spatial and problem skills by solving complex Tangram-style puzzles.

Representations in Tile Farm Academy’s Daily Challenge

Tile Farm Academy’s Daily Challenges teach students everything from counting to multiplication to order of operations in a unique way that involves students playing games and solving puzzles that incorporate diverse representations of numbers.  Learning math in the context of a wide variety of representations allows students to develop a deeper conceptual understanding of math, and trains students to become flexible thinkers capable of applying math they have learned in a wide variety of real world contexts.  Ultimately we aim for students to not only learn basic math, but to see how universally useful math can be.  

In Match Maker, students think flexibly and develop their numeracy skills as they match diverse representations of numbers.

Connections in Tile Farm Academy’s Bright Ideas

Tile Farm Studio is all about seeing connections.  Time and time again we have seen students make connections between math, art, and the real world through their creations in Tile Farm Studio.  This ranges from kindergartners building their favorite cartoon characters, to summer interns building the 20 genetically encoded amino acids, to professional graphic artists designing logos in Tile Farm Studio.  One of the best ways for students to practice using Tile Farm Studio is in Tile Farm Academy’s Bright Ideas.  Bright ideas are a daily activity that encourage students to use their creativity as they discover the connections between math and art.  After completing their bright idea, students have the option of turning their design into real world products in the TIle Farm Maker.

The design shown above was made by two brothers ages 4 and 8 in response to a Bright Idea prompt asking students to build a geometric representation of their favorite cartoon character.

Communication While Building in Tile Farm Studio

While math is often traditionally thought of as an “individual” subject, adding a social element to math learning not only makes it more fun, but also is a great way to develop students’ communication skills.  One of my favorite things to do with students is to let them freely build in Tile Farm Studio, then ask them to collaboratively describe, analyze, and discuss each other’s creations.  This activity is fun to do in a family or classroom setting, and is great for developing students’ vocabulary while also teaching students about the diversity of human cognition.  

Shown above are diverse representations of the number 42 made by students in Tile Farm Studio.  Discussing patterns like these are a great way to develop students’ communication skills.  What do you notice about these creations?  What do they make you wonder?  How are they similar?  How are they different?

Proof and Reasoning in “Is it Possible?”

One of the most valuable lessons I learned in my years working as a scientist is that not everything is possible, and it often requires rigorous proof and reasoning to demonstrate this.  Tile Farm Studio makes this type of proof and reasoning accessible to users of all ages, as it can serve as a playground to hypothesize, experiment, and play with math.  An activity I love to do with everybody ranging from my father who has a Ph.D. in math, to my four year old nephew is play “Is It Possible?”  This involves giving each other prompts for something to build in Tile Farm Studio, and then either proving the prompt is possible by building it, or use reasoning to determine if it isn’t possible.  For example, with my nephew I might ask, is it possible to make a triangle only using trapezoids?  Meanwhile, my father still has an unanswered hypothesis, is it possible to build a convex shape out of pieces that have C2 symmetry that does not have two fold rotational symmetry?  This activity is fun for users of all ages, and provides a valuable opportunity to develop students’ proof and reasoning skills at an early age.

Is it possible to build a triangle only using trapezoids?  Is it possible to build a square only using trapezoids?

Are you interested in providing your child with a math education experience that prepares them to succeed as problem solvers in an ever changing world?  If so, sign up for a Tile Farm Premium account today!

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Alex Romero, Chief Experience Officer

Alex has an MS in biochemistry and molecular biophysics from Caltech, and has extensive experience both as a research scientist and as an elementary school math and science teacher. He is passionate about art and innovation, and making the math learning experience as beautiful as possible.