Education Reviews · PhD Life · Science of Disney · Uncategorized

Mythbusting Mr. Incredible’s “New Math”

“Why would they change math?! Math is math! MATH is MATH!!” Bob Parr (aka Mr. Incredible) protested in Incredibles 2.

Most people who enjoyed or are heading out to buy the Incredibles 2 (released November 6th, 2018) will likely laugh at this joke. The joke works because so many parents today are struggling with the changes brought about by Common Core math. But is Common Core deserving of all of the jokes at its expense?

Although I sympathize with parents’ difficulties with helping their students with these “new” math problems, as a PhD student studying math education and math teacher education, I also want to share my knowledge about why Common Core math is a change for the better and also not much of a change at all.

Math Education Reform in the 1960s

The Incredibles and Incredibles 2 are set in the early 1960s, a time in which a different math reform called “New Math” was underway. New Math was a movement spurred by the launch of Sputnik and the United States feeling like they were falling behind the Soviet Union in a global competition for success and innovation (which had few tangible measures). The curriculum for new math wanted to enhance students’ conceptual understanding of math – knowing why standard algorithms work – rather than just procedural understanding – knowing how to do a standard algorithm.

Much like what we refer to as “inquiry learning” today, New Math wanted students to try and solve problems before being given the so-called rules, or standard algorithm (this practice is very common in math classes in countries like Japan whose students consistently earn higher scores than American students on international exams). Advocates of New Math argued for less repetitive drilling and instead for math that looked more like what mathematicians did – finding patterns and engaging with ideas like set theory and number theory. Even in this era, parents and teachers bemoaned the new content and strategies for teaching the content that involved more hands-on learning with objects rather than pen and paper arithmetic that they were used to.

Although New Math was effective in shifting the amount of time spent on arithmetic towards incorporating more advanced topics like geometry and calculus, teachers did not receive enough support in the mathematical content to achieve the goals of the movement in their classrooms besides using logic games.

After the end of the New Math movement, the goals of school math continued to swing back and forth between conceptual and procedural understanding, coming to a head in the so-called “math wars” of the 1990s, partly instigated by the Nation at Risk report which again highlighted how the United States was falling behind the rest of the world. Over the course of the decades between New Math and today, research in math education and the psychology of how we learn has made leaps and bounds and has been trying to impact what math looks like in schools.

Common Core in 2000s and 2010s

In the 2000s, the United States again felt like it was falling behind in several global economic indicators relative to countries like China, Japan, and South Korea as well as education leaders like Finland and Canada. The Common Core State Standards were seen as one important step towards preparing our students for the jobs of the future by again foregrounding conceptual understanding. Unfortunately, there are several myths about what the Common Core is and is not. I want to help dispel some of these so that parents and students alike can see how Common Core has not changed math in a negative way.

Myth 1: Common Core is a national curriculum.

This is false! First, the Common Core is not a curriculum.

The Common Core is a set of descriptions of what students are expected to be able to do in each year of school. They do not specify exactly what the content should be to help students master the set of skills nor do they specify exactly how teachers should teach it. To put in terms that the super-speedy Dash Parr would understand, the Common Core is determining where the finish line of the race is – not telling racers how they have to run, what equipment they have to wear, or whether or not they can use their superpowers.

Secondly, the Common Core is not federally mandated.

The Common Core was developed independently from the United States federal government by a bipartisan committee sponsored by a collection of governors and non-profit organizations. Before the Common Core, states were extremely varied in the race they were expecting their students to run. The developers were just trying to make sure the finish line was in the same spot for students in all 50 states so that a student who excelled at the 100-meter-dash wouldn’t be expected to run a mile if they moved from one state to another.  Furthermore, before the common core, it was difficult to compare proficiency levels across states. Continuing the analogy, a student who ran a 20-minute mile might be classified as “super” on one state’s assessment, but “not super” in another state because that state defined “super” as running a mile in less than 10 minutes.

After the standards were developed, states were able to choose whether they wanted to adopt these standards – and the standardized tests that accompany them – or not. Currently, only 43 states are using Common Core standards; several states declined to adopt them or have declined to use the standards-aligned tests. Instead, they’re developing their own standards and tests (that are often built on and look very similar to Common Core).

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Image from CoreStandards.org

The national government under Obama did have an effect on how many states decided to adopt Common Core though because they sponsored a competition called Race to the Top for states and school districts to receive bonus federal funding. To enter the competition and receive money, a district had to demonstrate how it was going to align with the Common Core standards, whether with curriculum or assessments. They had to provide some evidence that they were going to expect students to run the race with the finish line set by the Common Core.

Myth 2: Common Core is part of the Democrat agenda.

This is false also!

I will repeat that the The Common Core was developed by a bipartisan committee and underwent revision from people on both sides of the political divide. Several conservative organizations like the Fordham Institute (a research organization) and former Florida Governor Jeb Bush support the Common Core because they acknowledge the positive outcomes that are associated with raising our expectations of schools. And several liberal figures and organizations like the National Education Association oppose the Common Core because they do not support standardized tests in general or are worried about the impact the change will have on teachers.

Although I am not sure where Mr. Incredible stands on the role of the federal government or liberal vs conservative ideals, I think more of this complaints about math reform would fall under the umbrella of the next myth.

Myth 3: Common Core makes math harder and more complicated.

Many of parents’ complaints that can be found online or in everyday conversation are that the procedures encouraged by the Common Core math standards are extremely inefficient or ridiculous. Frustrated parents think it is more important to get the correct answer to a problem efficiently than to show their work using these complicated procedures.

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The main mistake is that Jack subtracted 306 (3 groups of 100 and 6 groups of 1) rather than 316 (another group of 10).

To these parents I want to say: although some of the procedures may involve strange steps or seem silly, having students solve problems in these ways or in multiple ways helps them achieve conceptual understanding, which is better for them in the long-run (Richland, Zur & Holyoak, 2007; Rittle-Johnson, Star, Durken & Loehr, 2018). Common Core makes math different, not necessarily harder, and is supported by research in math education about how learning the reasons why the efficient algorithm works is better for retention and problem-solving. With the new standards, students are expected to be able to explain and critique (two skills which are more highly valued in the workplace) different methods for solving problems rather than just memorizing one way.

But what about the fact that test scores have gone down since Common Core was implemented?

Yes, scores on yearly assessments have dropped in the first few years of implementing Common Core and this can be interpreted as evidence that Common Core makes math harder. But the tests that have been developed to align with the Common Core standards are considered to be harder partly because they are unfamiliar and ask questions in different ways than the ways students are used to being tested and the way teachers are used to teaching.

This last piece about how teachers and their teaching has been affected by the Common Core is one of the main reasons that I am critical of the Common Core. In many places, teachers have not been provided with enough support for successful implementation. Teachers have to master the very skills that they are expected to teach their students because their math education did not teach them in these ways. Teachers also have to learn new ways of teaching because along with new skills come new misconceptions and mistakes that learners are likely to make. Teachers have spent a lot of time figuring out how to best instruct and help students with mistakes related to the standard algorithm. Now, teachers need help with identifying and remedying the kinds of mistakes that students make when asked to solve problems that align with the Common Core.

But what about parents?

Unfortunately, this does not help parents much because they, like Mr. Incredible, still want to help their kids but aren’t receiving the kind of training that teachers have access to.

Websites, guides and books have been popping up to offer parents assistance with Common Core. But parents don’t need to become experts in Common Core methods; sometimes it can just be better to ask kids about their thinking and discuss it with them. Making claims and defending them is one of the most important skills that the Common Core tests assess, regardless of age level or math content area. Furthermore, try not to pass on math anxiety and instead foster a positive math environment by playing math games or showing your child how you use math confidently in your everyday life. One of the most effective ways to help your kids with math is to promote a growth mindset – the idea that intelligence or success, especially in something like math, is not pre-determined but rather can be developed through effort and a positive attitude – by praising your child for not giving up and trying their best. In my own tutoring of high school students, I find that just expressing enthusiasm for math and how cool I think it is when I realize a new aspect of how math is interconnected can go a long way.

The Future of Common Core

Social scientists in academia and in policy are doing a lot of research on how these new standards are changing the lives of students. Some places are showing signs of success, like closing the achievement gap between more and less disadvantaged students. Research is also being done on improving teachers’ ability to teach Common Core, which doesn’t mean having them just take more math classes, but rather understand the connections among math content areas like students are expected to do. More work still needs to be done on how to effectively help parents become more capable and confident with Common Core. One of the first steps towards helping students is acknowledging the historical precedent for Common Core math and embracing the new ways of solving not as infuriating challenges to adults’ superpowers of patience but rather as incredible opportunities to learn together.

Additional reading

Vox has a great explanation of the Common Core

NPR has a Common Core FAQ as well

Disney Trips · Education Reviews · Uncategorized

Science Behind Pixar Museum Exhibit Review

Since starting my PhD in Learning Sciences, I’ve taken quite a few classes that have been focused on the design of learning environments and museums in particular. So I have become overly critical of museums and museum exhibits as learning opportunities because I am now better equipped with theories and ideas about what educational goals the designers were intending to achieve and how they were trying to do so.

Even with this more critical perspective, I think the Science Behind Pixar exhibit at The Henry Ford was the best museum exhibit I have ever experienced. Even if you aren’t a huge Disney or Pixar fan, I highly recommend going to see the exhibit in its next location (it is set to close at the Michigan location after March 18th) or at least check out the website that has a majority of the activities available online (linked below) because you’ll learn a ton about movie-making in addition to applications of science and math that you may never known about.

Overview

The entire exhibit is meant to showcase the combination of art, math, and computer science that enables Pixar to create their award-winning movies by telling the stories of how a movie gets made. Additionally, one of the explicit and NSF-funded goals of the exhibit was to support novice learners in understanding computational thinking, specifically problem decomposition.

These goals are accomplished through nine themed areas aligned with nine departments of Pixar Studios:

  1. Story & Art
  2. Modeling
  3. Rigging
  4. Surfaces
  5. Sets & Cameras
  6. Animation
  7. Simulation
  8. Lighting
  9. Rendering

After watching an introductory video that highlights the majority of the content dedicated to Story and Art, museum visitors enter the Modeling department and proceed through the rest of the departments at will. In each department, there are videos and interactive activities centered around a Pixar challenge that had to be resolved using math and science. The videos include interviews with Pixar employees about their childhoods, their jobs and about the math and science they used to solve the challenge in their department. In each department, there is at least one guided exploration activity and one more open-ended exploration activity designed to give visitors hands-on experience with solving the challenge for the department.

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Some of my favorite activities for their content and engagement were the Programming Natural Variety in Sets & Cameras, Surface Appearance Workstation in Surfaces, and Crowd Simulation Workstation in Simulation which will likely be getting their own blog posts soon!

What Was Done Well

The overall story and flow of the entire exhibit really gave a nice direction to the exhibit as a whole. The introductory video (also available on the exhibit homepage) outlines the various jobs of the departments at Pixar that contribute to making a film – the same jobs that you’ll get to try a hand at in the exhibit. With each activity having at least two workstations, multiple people could be engaging at the same time which increased the capacity of the exhibit and encouraged interaction among visitors among and between parties.

The effort put forth to really make this a family-going experience was apparent in all of the elements of the exhibit. Each video and screen-based activity also had a transcript and audio recordings of the instructions so that blind, deaf, or hard-of-hearing patrons can have equal access to the content. One of the aspects that I appreciated most was the presence of stools in front of many of the videos and activities and the placement of the video screens at more of a kid level than an adult level; providing the stools allowed adults to get down at the kids’ level for more intimate interactions, to provide a lap for smaller children, or to just rest their limbs for a lengthy exhibit experience.

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Additionally, one of the strongest and most consistent arcs throughout the exhibit were the stories from the Pixar employees about how their childhood and passions shaped their career. From mentions of the computer program Logo to breaking an expensive camera apart to figure out how it worked, these personal touches were clearly intended to inspire younger visitors to lean in to their hobbies and keep dreaming of one day working for Pixar. Knowing more about the various positions at Pixar can help kids figure out career aspirations in STEAM fields that they might otherwise never know existed.

The science and math content was foregrounded in each activity with brief descriptions and diagrams. Science content included the physics of light and color and materials as well as engaging in experimental practices like making predictions and testing variables systematically. I learned about applications of 3D coordinate planes, angles of rotation, how to create 3D objects from 2D shapes, the Monte Carlo simulation, and mathematical patterns in nature to name a few.

The activities were designed with several learning principles in mind. Leveraging the power of story-telling for learning, the linear nature of the exhibit made it more memorable and the pieces building on each other scaffolded visitors to build integrated knowledge structures.

The activities were both authentic and exploratory, which, according to constructionism and inquiry-based learning, are some of the main requirements for a successful learning experience. In particular, the open-ended activities allowed visitors to apply and further hone their understanding of the math and science principles to create and experiment with tools that Pixar employees would actually use. For example, the Programming Natural Variety activity involved adjusting parameters to generate grass with different appearances which seamlessly integrated randomization and scientific research on nature’s mathematical patterns.

Furthermore, the exhibit used several comparisons (what my PhD research focuses on, so I’m biased!) to demonstrate the power of the technology for telling better stories such as subdivision and surface refraction contributing to more realistic characters and lighting significantly altering the mood of a scene.

 

What could still be improved

More inclusion of more recent movies

I was disappointed to not see more from Pixar’s Coco but the exhibit was designed before the movie came out. Cars 3 which has also received lots of praise for featuring Cruz Ramirez as a female protagonist and Finding Dory were also not included (although there is a large model of Dory for one of the activity stations or to take pictures with). If you or your child are going in with the expectation of seeing these characters or learning more about the technological advancements for these movies, you may be disappointed.

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More resources for parents and educators to use with their children in the space

While several of the interactive activities are accessible and engaging for learners of all ages, providing at least some questions for adults or children to ask of each other would likely spark more conversation and curiosity around the math and science content. I found myself asking one child who was trying to achieve a spooky mood for the Up lighting activity, “How did you do that?” and I think having more questions to get kids to explain their learning and processing can help them take away more from the experience.

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More detail on some of the science or resources to follow-up with to learn more

My interests were definitely piqued but I found that the “More Info” buttons included in some of the activities did not provide enough of a detailed explanation of the science and math underlying the technology. While my desired level of understanding may not align with that of the target audience, having these materials more easily accessible in a pamphlet or more obviously linked on the website would be helpful to other curious attendees (The Pixar in a Box on Khan Academy seems to have the most in-depth and germane resources but I had to click beyond the front page to find it). Including some scannable QR codes to more in-depth explanations would have also been a modest yet helpful addition.

More representation of minority employees and characters

While Pixar has recently said that they aim to include the voices of more women and people of color in their company and products, this was only somewhat represented in the exhibit materials. Several of the video interviews with employees were with white males and people of East or South Asian descent who are stereotyped to be good at math and science; I only recall one black woman and she was an intern and not yet a full employee. As the company moves towards more diversifying the workplace, some more interviews can be done and hopefully more of the movies will center around characters whose stories have not yet been featured on the big screen.

More Resources

The official exhibit website has several of the videos that can be seen in the exhibit for people that cannot attend or for those who want to get a better idea of what to expect. Most of the content of the exhibit is available online except for some of the Animation activities that required physical interaction such as to create a stop-motion video of Luxo Jr. jumping.

The webpage for educators has several resources for teachers and parents alike to use with their children. Many of the laudable inquiry-driven activities from the exhibit are available online in full (I found that they worked better in Safari than in Chrome) and there are some additional activity cards with guiding questions to ask students.

The Pixar in a Box collaboration with Khan Academy is surprisingly extensive. There are a handful of sequences of videos and activities around story-telling, simulation, color science, virtual cameras, effects, patterns and more science and math topics. I have not had time to completely explore it but I am usually skeptical of Khan Academy content because it is predominantly lecture-driven and the questions and activities aren’t much of an improvement over inauthentic, rote worksheets. At a glance, the Pixar touch likely makes it more engaging and productive than what I might usually expect from Khan Academy.

The webpage for researchers has direct links to the purposefully designed computational thinking activities and information about posters that were presented on research done in the exhibit. Some of the posters feature more details on the demographics of the research participants and the vast majority are Caucasian. I hope that more efforts are being made to recruit more students and families of color to attend the exhibit. More research should also be done on whether the online materials are being used by similar populations.

Ask a Pixar Scientist allows curiosity to continue beyond the exhibit by publishing kids’ and adults’ lingering questions with responses from actual Pixar employees.

 

Let me know what resources and activities you thought were the most fun to play around with online or in-person or which ones you’re most curious about learning more about!