Chefs Know More Than Just Recipes: How Experts Differ From Novices

By Tim Hudson

Chefs Know More Than Just Recipes: How Experts Differ From Novices first appeared on the DreamBox Math Learning Blog, on April 15, 2014

Many years ago I surprised my wife by cooking a new meal. I read through our entire Betty Crocker cookbook to find just the right recipe and went to the store for the ingredients we didn’t have: ground cayenne pepper, white vinegar, and ginger root. These items are forever stuck in my memory because they were unfamiliar to me and therefore seemed unusual. At the time, I didn’t know there were different colors of vinegar, and ginger root looked so bizarre that I boldly asked the clerk at the register, “How many people actually buy this thing?” In hindsight, it was an embarrassing question to ask for a number of reasons; the least of which is because as it turns out, fresh ginger is delicious. Looks can be deceiving.

The great thing about cookbooks is that they are designed so that culinary novices—like myself—can accomplish one narrow task (prepare a recipe). Culinary experts can certainly use cookbooks too, but they’re not typically designed for expert chefs. And importantly, cookbooks are not designed to enable and empower novices to become experts, but rather to provide explicit instructions for what to do in the kitchen. I’ll discuss more about novices and experts in a moment because it’s as important for learning cooking as it is for understanding mathematics, and really any subject area. And if you’d like to learn more, the second chapter of the book How People Learn is actually entitled “How Experts Differ from Novices.”

Thanks to the clear instructions in the cookbook, I was able to follow the recipe. The meal was amazingly delicious and over the years I’ve cooked it dozens of times. In fact, I’ve cooked it often enough that I now know it from memory, and I don’t even need to review the recipe. I never specifically sat down and memorized the ingredients or steps word for word, but through repeated use, the recipe has become a part of my acquired knowledge. The key to the recipe seems to be the sauce, where chicken broth, sugar, soy sauce, cornstarch, white vinegar, and ground cayenne pepper are mixed together.

As an educator, I can’t help but reflect upon what my knowledge of this recipe and the ability to create the meal from memory indicates about my deeper understanding of food and chemistry. Does the fact that I can execute this recipe perfectly every time from memory serve as evidence of understanding, or is it simply a skill that I’ve acquired through repetition but without comprehension? Exactly what do I understand about cooking, ingredients, and their interrelationships within the recipe? Truthfully, as an assessor, I believe that the answer is, “Nothing.” I’m very much a novice in the kitchen in general, and even though I can repeatedly recreate this one specific recipe with ease and delicious results, I am by no means an expert.

For example, using sugar, chicken broth, soy sauce, and cayenne as ingredients makes sense to me because I know what they taste like individually. But I don’t understand why they need to be added in the ratios called for in the recipe. Or why—when combined with garlic, ginger root, cornstarch, and white vinegar—they taste so good. Over the years I’ve been told by others that cornstarch thickens the sauce. I can see that the sauce does thicken, but how do I know that’s not a result of the soy sauce or sugar? I’ve never tried making the recipe without cornstarch, so to believe the “cornstarch thickening hypothesis” I just trust what others tell me. I didn’t ever make sense of the “thickening theory” on my own, so I can’t really understand it. Also, of all the ingredients, the white vinegar makes the least sense to me. To begin with, I don’t really know what vinegar is or even how it’s made. And until I read this recipe, I didn’t even know there were different kinds and colors of vinegar. Would the dish taste different if I used a different color of vinegar? Or would red vinegar change the color of the sauce?

Ultimately, I don’t really comprehend anything about the recipe, except how to follow the steps. And although I don’t understand the reasons for the steps, I trust them because they are coming from a reliable source, and I can observe that they work when I follow them. Based on my rote knowledge of the recipe, I can demonstrate skill in executing it, but I have no true comprehension or understanding of the relationships between the ingredients or any reasoning behind the processes or order of the steps. If I were attending a culinary school, what might be done to help me deepen my expertise as a chef?  I would expect that it would be something different than simply more practice following recipes.

Many students feel the same way about math as I do about cooking. Though they probably don’t think an expert chef is someone who has simply memorized a stack of cookbooks, they likely believe that mathematical expertise is demonstrated by knowing multiple algorithms and remembering an ever-increasing list of confusing procedures. Their understanding of the multiplication algorithm or quadratic formula is often at the same novice level as my understanding of cooking; their typical questions are: What’s a placeholder? Why am I carrying a 2? What would happen if I went left-to-right instead? Why do I take the square root? Why must that b value be negative?

It’s not enough for our students to be novices in mathematics, because the goal of learning is transfer and independent use in new situations. I imagine that’s why cooking reality shows and competitions don’t simply give a group of contestants the same recipe and ingredients and ask them all to prepare the same dish. Instead, contestants are presented with complex challenges and restrictions without instructions that require critical thinking and expertise.

Novice cooks follow instructions and execute with knowledge and skill. Expert chefs do that, too, but they also invent new recipes based on their understanding of ingredients and methods. We need all students to be “expert chefs” with numbers, algebra, and mathematical reasoning. Which means they’ll need more than a “math cookbook.” No amount of isolated skill practice or following procedures without understanding can cause these critical learning outcomes. Students need thought-provoking challenges, sense-making experiences, and the opportunity to develop understanding that will empower them to cultivate true expertise in mathematics.

New – Google Classroom This Fall

Man vs. Machine: 4 Robotics Programs for STEM Classrooms

If robots are ever going to take over humanity, it’s going to be an uphill battle. Undoubtedly, the engineers who create them will be tough to match wits with, at least if they come from the STEM labs in our classrooms today.

Research shows that robotics is an effective tool for improving students’ 21st century skills. And teachers have taken note. In various school settings and across all grade levels, students are engaging in programs teaching them to design, build, and program their own bots. As they do, they are developing their creativity, collaboration, self-direction, and communication skills too. So whether you want to prepare your students to withstand the bionic revolution or hasten its coming, the following educational robotics programs will serve you well.

LEGO Mindstorms

When it comes to school robotics programs, LEGO Education is the big fish in a little pond. Their Mindstorms robotics package, designed for upper-elementary and middle school students, is a natural extension of a childhood love of LEGOs. A computer-based brick, specialized LEGO pieces, a swath of sensors, and programming software, Mindstorms kits power 21st century learning without the accompanying learning curve of new technology. Not only are classrooms and after-school clubs utilizing LEGO Mindstorms for their ability to boost students’ interest in science and technology, many of them have formed teams and compete annually in FIRST LEGO League challenges which take place locally across the country.

WeDo

For early elementary students who won’t wait for middle school STEM classes, WeDo (also by LEGO) will help to create learners who don’t just know about robotics, but do robotics. Designed specifically for the early emerging engineer, WeDo enables teachers to tailor activities to specific curriculum subjects or project-based learning. A simplified version of LEGO’s Mindstorms offering, WeDo comes with a user-friendly software interface and a “plug’n’teach” activity pack that helps teachers cover science, technology, engineering, and mathematics in an engaging hands-on, minds-on way.

Sphero

If your focus is on programming robots rather than building them, Sphero might make you feel magical. At the very least, its going to make you forget that you’re really just playing with a ball. As the name implies, Sphero is a sphere. But it’s one that you control from your iOS or Android device. Make Sphero move, spin, change colors, and more. “Sphero is an interactive and engaging robot that brings programming off the computer and into real life.” With over 25 apps now available for Sphero 2.0, robotics enthusiasts are using Sphero to drive through homemade racecourses, turn their classroom into an augmented reality video game, and engage classmates, friends, and family in multiplayer fun. If you can pry it out of your students’ hands, you will see why Orbotix says that Sphero is “One smart ball [with] infinite ways to play.”

Play-i

Play-i is so 21st century that it’s not even out yet. Still this crowd-funded project has been popular enough that over $1 million worth of pre-ordered Play-i robots sold out in the first month they were available. To get your hands on your own, you’ll have to order now in time to get Play-i by Christmas 2014. But when engineers from both Google and Apple get together to teach kids how to code, the wait for what they made is definitely worth it.

What everybody wants, but nobody has is a duo of robots that fuse storytelling and play with programming. Bo, a mobile three-wheeled bot, and its stationary sibling, Yana, teach kids how to code through narrative. Controlled via Bluetooth-based remote app, children as young as five can learn to use Play-i by looking at and touching the script on an iPad. Bo and Yana can sense each other, respond to objects, play music (literally. . .on a xylophone), and even deliver a freshly picked flower to a friend. But most important, the Play-i robots help kids learn about if-then code without requiring them to master a programming language. It gives them access to computer science education before they’re even old enough to know what that is.

Whether or not our good intentions will lead to the demise of mankind is yet to be determined. But with the opportunities to engage in STEM-based learning listed here, at least we can ensure that our downfall will be fun.

Lest our fears get the best of us, it’s important to remember that even Isaac Asimov, the face of futuristic science-fiction writing said, “I do not fear computers. I fear the lack of them.” Additionally, the author of Robots and Empire believed that “The true delight is in the finding out rather than the knowing.” So, instead of protecting ourselves from our own creations, here’s to our blissful ignorance of a potential apocalypse, even if it is one LEGO brick at a time.

Rethinking Math Teaching

9 #EdTech Problems You’re Facing

Technology in education isn’t new, despite what it might feel like. The Internet is older than most beginning teachers and depending on how you define “technology,” you have to admit that it’s always been an iterative change process.

However, it does seem as though we’re finally at a breaking point where our old systems have stretched to their absolute capacity for the influx of new technologies. In layman’s terms: we’re maxed out and something has to change. Here are 9 problems that #edtech needs to fix, in 3 categories: #1-3 are about Communication, #4-6 are about Visibility, and #7-9 are about Pedagogy.

1. Parents. No, not the parents themselves, but rather our communication channels with them. We need better methodologies in place to have open, honest, transparent conversations with the parents of the students we teach. Involving parents in the educational process is the single greatest contributor to an increase in student achievement.
2. Students. I’m sure education would be much easier if we just had robots for kids, right? But that would be boring and that’s not our world. Nobody signed up to be a teacher because it was easy and that would be a waste of our talent. Instead, we need an edtech solution to how we can keep communication channels open with our students about their learning. Much like we need more dialogue with parents, we need students as active participants in their own learning as well. Students need to have voice and choice when it comes to their learning and so far, edtech has provided a lot of choice, not so much voice. Tools like Remind101 and Edmodo are changing the paradigm around the conversation of student learning and I encourage others to follow suit.
3. Universal IEPs. This is a problem you probably didn’t know we had. Here’s the scenario: students identified as qualifying for special education services have a meeting once a year where their teachers look at the instructional practices that work or don’t work for that specific student. They set goals for the year and identify any new strategies that could be tried. They talk about the future of this specific child’s education and, as a team, commit to working together for their benefit. Oh, and did I mention that the student is part of this process as well? They are in the room while this is taking place, interacting with these educators, administrators, diagnosticians, and their parents. They are actually a co-creator of their learning. Why don’t all students get this? Time and money. This represents the single biggest opportunity of edtech, in my humble opinion. Show me a tool that provides easy pathways to have a conversation about a specific student with all of their stakeholders with identifiable outcomes and recommended practices for the upcoming school year and I will show you a billion-dollar idea and one that will completely change the face of education.
4. Data. Teacher-accessible data that is clear and easy to understand just doesn’t exist. Data analysis is right up there with ‘root canal’ in most teachers’ prep times. And let’s not even start down what data visibility looks like for students and parents (it’s nonexistent). Companies like Eduvant and Metryx are looking to change this, but the edu-pool is big enough for all to play in. Let’s stop talking about data-driven decision-making and actually do it.
5. Soft Skills. Remember, back in the day, when we had character education? For some, it was even a class! We’re pretty focused on cognitive skills (reading, writing, arithmetic) but we’ve passed the buck on our non-cognitive skills like empathy, respect, and leadership. Yes, we could point fingers at why we think these skills have fallen by the wayside, but the past doesn’t have to determine the future: we can choose to value these again and edtech can help. We need tools to help us track and identify the impact of these skills. We need to be able to demonstrate them and show employers how valuable our skills are: cognitive and non-cognitive.
6. Lesson Planning. Somewhat surprisingly, we still need edtech to step in when it comes to lesson planning. We need embedded state standards. We need collaboration. We need idea discovery mechanisms. We need sharability. We need transparency. There is so much opportunity here and I am excited to watch companies likeTrinket, Planboard, and Common Curriculum as they seek to innovate this space.
7. New tools. This one might seem a little ‘meta’ at first, but hang with me. Teachers need to know what to use in their classroom and how to use it. It needs to be easy and it needs to be fast. Please don’t tell a teacher to go to a conference or “search the Internet” or “join a Twitter chat” to find the latest tools. Yes, these will work, but they are horribly inefficient. Keep an eye on great tools like EduClipper and what they’re doing in this space.
8. Entrepreneurialism and the Maker Movement. Teachers desperately need help here. If we want to see more entrepreneurs and more makers, we’ve got to create the spaces for our students to not only discovery but develop these skills. For this to happen, there need to be the resources in place to facilitate this kind of learning. It represents a pedagogical shift for sure, but education is ripe for this kind of innovation and we think the edtech community is primed to bring it. Here’s the bottom line: if you want entrepreneurs and/or makers and you are one, you need to create something to help expand the playing field. You need to get more folks into the game, not less.
9. The Nature of Learning. The massive influx of personal computing devices into classroom environments represents a tidal shift in pedagogy. If we want teachers to be successful with these pedagogical shifts, we need to give them the support and resources they need to make them. More than just an app or a tool, teachers need training and practical steps to help them cross this chasm.

The 21st century is here and it’s brought some baggage. How will you turn it into an opportunity? Teachers, which of the above most resonates with you? Be sure to leave some feedback for us in the comments.

Boost Science Literacy with Music

If you ever watched Bill Nye the Science Guy, you probably remember the song parodies his episodes featured, which rewrote the lyrics of popular songs with scientific themes. Sure, getting the song stuck in your head will probably help you remember a few facts, but the benefits of music to learning science could go beyond just helping your memory.

Check out this recent article from the University of Washington, which suggests that music can help you learn science not necessarily by including mnemonics, but by relaxing and engaging you. After you read that, check out SingAboutScience.org, a database of thousands of songs about science and math. Their navigation isn’t the most obvious–search for songs under ‘Find/Add Songs’ and click on the little purple buttons by each song.

A few of my favorite songs about science from around the web: Fossil Rock Anthem, Bill Nye’s Air Pressure, Large Hadron Rap, Biologist’s Mother’s Day Song, anything from Symphony of Science and a lot from Geek Pop. And let’s not forget They Might Be Giants’ entire album of science-themed songs called “Here Comes Science” (check out my favorite song on the album: Why the Sun Really Shines).

New! Blended Learning Infographic

This infographic first appeared on Navigatorfrom CompassLearning on March 24, 2014. 

Bended learning incorporates multiple methods of instruction in order to customize the learning experience for each student, leading to increased student interaction and engagement. A critical component of a rigorous blended learning model is quality digital learning time, filled with digital curriculum aligned to classroom curriculum. Learn more about harnessing the power of digital curriculum in the blended learning classroom in this new infographic by Compass Learning.

10 Things to Consider When Choosing Digital Tools for Students Ahead of the Curve

Originally posted on GettingSmart Blogs

By: Catelyn Cantrell

Engaging study materials—whether print or digital—seem to be geared mostly toward students who are struggling. This is without a doubt a positive and necessary trend, but there is no reason to support one group and not the other. In fact, some tools work for a variety of student populations.  What I want to talk about is how to recognize and select tools for the students who are working beyond their grade level. Digital tools enable strong students to direct their learning to places outside the restrictions of the conventional classroom setting.

1. Purpose of the Tool. Before considering anything else, each digital tool selection should be made with a clear purpose in mind. Is the tool meant to prepare the student for standardized tests or is it meant to help students explore their more creative side? Although some tools may end up being used for multiple tasks, a specific goal is key to maximizing the tool’s value. It all begins with a single, simple question—What can the student do with the digital tool?

2. Context: Classroom, Home or Something New? Consider where the tool will be used. The context in which the tool is used will shape how the student uses  the tool.

3. Is the tool required or just something extra? Once you know the purpose and type of tool you’re looking for, determine how the tool will figure into the student’s existing inventory of tools. Is this tool going to be required for a class or other academic program? Is it just an extra way for the student to explore topic not covered during class? Figuring out these questions also help inform cost and time considerations.

4. Individual or Collaborative? Is this tool meant to give students a sense of community or is it meant for individual work? Some digital tools might provide those students at the top of the class a chance to connect with similar students. Educational technology affords them the chance to build not only academic abilities, but also the social skills at the heart of the learning process.

5. Costs and Savings. The cost of the tool is (of course) another factor to consider. Free and cheaper software is easier to access and may have a larger user community. Also, a digital tool may actually end up saving money for schools, teachers and students. So the question may actually be about how much money the tool will save you, rather than cost you. If money is really tight, frame it as a learning experience and bring students into the conversation. Advanced students are often inclined to help solve problems!

6. Saving Time for Busy Students. Digital tools often save students and teachers more than just cash. Another thing to consider when comparing tools is whether or not they can make studying more efficient. Technology can help students learn smarter, not harder. Try to find tools that follow this idea. Advanced students often already have intense schedules, so why not find ways to make use of usually wasted time?

7. Familiarity with Technology. There should be a consideration about how comfortable the student is with digital tools. Think about tools they have used previously and how they compare to the potential selection. Even if the student lacks experience with digital tools, a new tool could be a valuable learning experience.

8. Personal and Academic Interests. It is important to think about the student’s strengths and interests. A tool can either allow a student to push their already strong skills to the next level or let the student work on an interesting, but unfamiliar subject. Technology is all about removing limitations and building connections. A quality digital tool should connect the advance student with new, useful content and experiences.

9. Chances to Explore and Create. Many digital tools also equip students with the freedom to explore their own ideas. As project-based learning becomes increasingly popular, these tools will be useful to advanced students as they embark on projects for class and those emerging from their own unique interests.

10. Feedback and Practice Opportunities. Digital tools can provide students with the chance to take risks with the material they are learning. Some can also provide educators and parents with insight about the real capabilities of their students.

Some digital tools also provide a more comfortable environment for practicing material. Often, more advanced students are reticent to practice material if they are unsure about it. A tool which provides useful feedback without any potential for low grades may be an appropriate choice for students to practice while also not worrying about test scores or embarrassment. Some digital tools also help students grow familiar with environments in addition to content. This works well for those bright students who are entering test preparation time later this spring.

Education technology crosses over barriers between learners and content. With this in mind, digital tools and advanced students seem meant for each other. A well-chosen digital tool will connect the advanced student with materials once outside the limits of their existing classwork. Always keep in mind that these students will often come up with their own ways to incorporate technology in their education. In fact, it’s second nature to most of them. So, be sure to include students in the conversation.  Make choosing the tool a learning experience in addition to the technology itself!

Making Math 3D

It is officially Mathematics Awareness Month, the perfect time to highlight what is making math more accessible and more real for students. 3D printers are definitely evolving into a essential tool for mastering mathematics in the 21st Century. In honor of the month, we are taking the opportunity to find out why.

When I think of 3D printers, I am instantly taken back to the days of George Jetson, imagine pressing a button and opening a magic door to exactly what I had asked for. Honestly, the 3D printing technology seems frighteningly close to that futuristic memory, but, the truth is, there is HUGE potential for 3D printing to impact math education in a variety of ways.

The Process. The idea of how 3D printing works is a math lesson in itself. Being a total novice in this department I calledCasey Hopkins, Founder of Elevation Lab. Hopkins uses a 3D printer to build product prototypes and was able to help me visualize the process – think of a tube of toothpaste or a hot glue gun, building layer upon layer until the desired object is created. Not to oversimplify, but in attempt to gain a very basic understanding of what is happening within these machines, he explained the process so that I could brainstorm classroom connections. It really breaks down to:

• The individual gives the machine a detailed set of instructions through the use of computer software (often including algebraic equations as instructions).

• The printer uses these instructions to create layers that build upon one another to construct the final project (think of building a ball by carefully stacking cut out circles of different shapes).

• In order to build more complex items, the software provides more complex instructions (and therefore more complex math to review with students).

The Mathematics. As you might have guessed, the math teacher in me can’t help but immediately think about how I would use this idea in the classroom, and the truth is there are a number of ways that a 3D printer can advance students conceptual understanding of fundamental and complex mathematics:

1. Functions – A 3D printer really is a perfect example of an input/output. Why not use the idea to help students understand the role of a function in mathematics?

2. Algebraic Equations – We can take the idea of a function one step further and look into exactly what equations are used in the computer software that builds instructions for these printers. If we want the printer to build a circle, what sorts of equations might we use in our instructions?

3. Recursive Formulas – This type of formula uses the preceding term to define the next term of the sequence. They may use the same formula but because they start with a different input, they result in different patterns.

4. (x,y,z) Coordinates – The final printed product is made up of a network of these coordinates that help to create the structure of the object.

5. Intersecting a plane with solid objects – When you intersect a plane with a cube, what do you get? Now think instead of building that cube out of a series of squares. Why not use the process of 3D printing to expand on this idea, better yet let the students research 3D printing and explain the process to you.

Mathematical Modeling. As I continued to research this idea, I wondered how else these printers would impact the classroom. For my continued education, I called our friend Dr. Matthew Peterson at MIND Research Institute. MIND Research is actively working on building 3D manipulatives that work with their Spatial Temporal (ST) Math software, helping “make math come to life even more so than with the software alone.”

MIND Research is currently piloting a program now that provides teachers with the software for a variety of manipulatives that are embedded into the ST Math program. Dr. Peterson explains that he has been looking at how to do manipulatives for a long time, “it adds a lot of flexibility and instant access into the physical world from a digital content.” MIND continues to research when and how to incorporate manipulates effectively to bridge between the physical and virtual world.

3D printing provides a more efficient model for a variety of classroom manipulatives. Most importantly, you can print out exactly each student needs. Gone are the days of purchasing full class sets and shipping them from around the world. If you have 30 kids that each need a hands on experience for different concepts, then you can easily personalize the learning experience for everyone of them. If you lose one piece, you won’t have to get a whole new set, you can instantly print just what you need. New technologies will allow you to recycle within the 3D printing machine, helping cut down on waste.

As the world around us continues to change, we need to look at how we introduce kids to new technologies and innovation. The 3D printer and other tools like it are creating more and more teachable moments for us and our students. Lets make sure we utilize these opportunities to help prepare students for careers of the future.

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