September 15, 2017

How to Turn a Word Problem into a Rich Math Task (Part Two)

How to Turn a Word Problem Into a Rich Math Task
Part Two: Crafting the Process

When students struggle in math, it's often due to their beliefs about what it takes to be successful in mathematics. They believe that some people were born with a gift for math, and anyone who wasn't born with that gift will never excel in math.

Fortunately, brain research tells us that this belief is nothing more than a myth, and it's not supported by fact. All students can experience success in math if they are taught in ways that foster the development of a mathematical mindset. This means setting high expectations for all students, engaging them in challenging and interesting math tasks, and providing the right kind of support and encouragement.

One way to foster mathematical mindsets is to replace simple word problems with "rich math tasks." Rich math tasks provide opportunities for students to work together as they explore a concept or solve a problem. In my webinar, Math Problem Solving: Mindsets Matter, I give examples of rich math tasks and share several strategies for using them with students.

If you're wondering how to get started with rich math tasks, it's easier than you might think. The first step is choosing a suitable math problem, and the second step is guiding your students through the problem-solving process. Both steps are equally important, so I've decided to tackle them in two separate blog posts.

In my first post, Part One: Crafting the Problem, I explained the difference between word problems and rich math tasks, and I shared 6 tips for creating a rich math task from a simple word problem. In this post, Part Two: Crafting the Process, I'll share strategies you can use to actively engage ALL of your students in the problem-solving experience.

September 7, 2017

How to Turn a Word Problem into a Rich Math Task (Part One)

How to Turn a Word Problem into a Rich Math Task
Part One - Crafting the Problem

Growth mindset is much more than a buzzword, and nowhere is this more apparent than in mathematics. Research findings in this field are transforming our perceptions about best practices in math instruction. As it turns out, developing a mathematical mindset is more highly correlated with future success in math than scores on standardized tests!

One way to begin fostering a math mindset in your students is to turn traditional word problems into "rich math tasks."

I tackled the topic of rich math tasks in my recent webinar, Math Problem Solving: Mindsets Matter, but I want to dig into rich math tasks a bit more here on Corkboard Connections.

Rich math tasks have two critical components, the WHAT (the problem) and the HOW (the process).

In this post, we'll take a look at how to transform a boring word problem into a rich math task. In my next post, I'll share active engagement strategies you can use to help your kids rock the problem solving process! Click here for Part Two.

How a Word Problem Differs from a Rich Math Task


Basic Word Problems
Word problems at the elementary level tend to be simple problems with a single correct answer. Children are often taught to solve them by learning to identify key words and numbers in the problem and then applying the necessary mathematical operation. For example, a basic word problem might read like this: "There are 10 apples, and it takes 2 minutes to peel each apple. How many minutes in all are needed to peel the apples?"
A typical method of solving this problem involves underlining the key words "each" and "in all" and circling the numbers 10 and 2. The key words tell students that they need to multiply the numbers to find the answer, so they multiply 10 and 2 and record the number 20 as the answer. If you ask these students to draw or model the solutions visually, they are at a loss. If you ask them to label the answer with the unit, they are as likely to write "20 apples" as they are to write "20 minutes." 

Word problems don't inspire deep thinking, analysis, or discussion because the solutions are fairly straight forward. Sure, you can encourage your students to talk with a partner about how they solved the problem, but their explanations will sound like this: "First I underlined the key words, and then I circled all the numbers. Next, I multiplied the numbers to get my answer." An explanation like that hardly qualifies as "math talk"!

Rich Math Tasks
Rich math tasks, on the other hand, are usually more open-ended and can be solved in many ways. Some math tasks are inquiry-based questions that have more than one correct answer or problems that require students to use hands-on materials to discover the solutions. Other math tasks look like regular word problems at first glance, but when you attempt to solve them, you realize there are many ways to arrive at the answer. Rich math tasks don't have key words that you can underline, and circling the numbers won't help because you might not even need all the numbers to solve the problem! These types of math tasks stimulate discussion, questioning, and critical thinking as students struggle to choose the best strategy to solve the problem.


6 Tips for Crafting an Awesome Math Task

Finding or creating the right math problem is the first step in developing a rich math task. Here are some tips that will make the process of crafting your problem much easier.

1. Start with a Visual Problem
Select a word problem that's easy to visualize, and try to solve it in several different ways. Make sure the answer can be represented visually by drawing it or by using physical models. If you realize that there's only one way to solve it or that it would be difficult to represent the solutions visually, rewrite the problem or find a new one. I'll use the Apple Peeling Word Problem above to demonstrate how to turn a simple word problem into something much more challenging and interesting.

2. Remove Key Words 
After you've selected a problem, look for key words such as, "in all," "each," "per," and "total." If possible, rewrite the problem without using the key words, making sure that the meaning doesn't change. Removing key words forces students to THINK about which operation is needed instead of just underlining words and mindlessly choosing an operation based on those words.

3. Add Extra Details and Information
Next, add details that aren't really needed to find the solution. If students have been trained to underline key words and circle numbers, these extra details will confuse them. They will have to think about the task and decide which words and numbers are actually important.

Let's use the first 3 tips to rework the Apple Peeling Word Problem and turn it into Apple Peeling Challenge #1. While the problem is still quite easy, the lack of key words and the extra numbers make it a bit more challenging. Students have to think about what is being asked and decide the best way to solve it. This is a good starter problem for introducing students to rich math tasks because it can be solved in more than one way using visual models. Students could draw circles for the apples, use round objects like pennies or bingo chips, or they could even use real apples!


Ready to take Apple Peeling Challenge #1 to another level? Applying the next 3 tips to that problem will make it even more challenging and interesting!   

4.  Personalize It and Make It Real
To make the problem more interesting, personalize it by adding a real person's name, maybe even the name of one of your students! Add enough details to make it come to life or turn it into a story. In Apple Peeling Challenge #2, including the detail that Sam is peeling the apples for a pie makes the problem more meaningful. A teacher in the Math Mindset Connections Facebook group took this problem and turned it into a story about making a pie for Thanksgiving dinner!

5. Turn It into a Multi-step Problem
Rewrite single-step word problems to ensure that multiple steps are needed to solve it. The information in the basic word problem stated that it takes 2 minutes to peel each apple. The easiest way to add another step is to replace that detail with enough information for students to calculate how long it takes to peel each apple. Each problem will be a bit different, but there's always a way to modify the problem and turn it into a multi-step math task.

6. Change the Numbers
You can often make a word problem more challenging by changing the number values. For example, instead of Sam peeling 10 apples, he might need to peel 100 apples because he's baking 10 pies for a banquet. You can also use numbers that result in fractional answers. For example, in Apple Peeling Challenge #2 above, Sam can peel 4 apples in 6 minutes so kids should be able to figure out how long it takes to peel one apple. But 6 is not divisible by 4, so the number of minutes it takes to peel one apple is not a whole number. Do you see how tweaking the numbers a little can instantly make the problem much more challenging? Now you have a problem that's perfect for a math task!

Why not try creating your own Apple Peeling Challenge? In the Math Problem Solving: Mindsets Matter Webinar, I shared 2 more apple peeling problems that are quite different from the problems in this post. I'll bet you can come up with your own apple peeling problems, too!


Where to Find Editable Word Problems for Rich Math Tasks


If you don't want to craft your own multi-step word problems, or you don't have time to hunt for them, check out my newest product, Math Mindset Challenges. It's a growing collection of editable word problems in several different formats. The problems themselves are in an editable PowerPoint document so you can change the wording and customize them if needed. All of the problems have been field-tested by upper elementary teachers, and they work well as is, but if you use a different measurement system or want to tweak the problems using the tips above, you can easily do that. If you'd like to take a closer look, head over to my TpT store and click on the preview link on the product page.


The Math Mindset Challenges product shown above is included in my Math Mindset Challenges Webinar Bundle and my Math Problem Solving Bundle. Both bundles include the Math Problem Solving: Mindsets Matter professional development webinar, too.


Next Up - Part Two: Crafting the Process

Remember that rich math tasks have two essential components, the WHAT and the HOW.  In this post, I've tackled the WHAT, the math problem itself.  However, it's not enough to create a great word problem; it's what you do with that problem that counts! Click here to read Part Two, Crafting the Process, where I dove into HOW to facilitate the problem solving experience. I shared loads of active engagement strategies that will take problem solving to a whole new level in your math classroom!



August 25, 2017

Mathematical Problem Solving: Mindsets Matter


Do you love math? Or are you convinced that the math train left the station without you long ago? No matter how you feel about it, if you're an elementary educator, you'll probably have to teach math at some point. Fortunately, growth mindset research and new findings about how the brain works are leading to some amazing insights about the best way to teach math. Furthermore, these insights are making it possible to foster a love of math in ALL students!

Last year I discovered Dr. Jo Boaler's book, Mathematical Mindsets, and I was fascinated by the research findings she shared. I also loved Dr. Boaler's strategies for using those research findings to improve math instruction. I know that problem solving is essential in mathematics, and most of the strategies I was using are supported by the new research. However, I did discover that a few of my teaching methods are not actually best practices, so I've been reworking those strategies to incorporate what I've learned.

A few years ago I presented a webinar called Math Problem Solving: Once a Day, the Easy Way, but after reading Mathematical Mindsets, I knew it was time to update that presentation with these new research-based practices. I asked Dr. Boaler for permission to include information and strategies from her book in my webinar, and she graciously agreed.

My new webinar is titled Math Problem Solving: Mindsets Matter to reflect the emphasis on growth mindset research and its implications for math instruction. To learn more, download the webinar note-taking handouts and take a look. The live webinar has ended, but you can sign up for the replay below. The replay of the August 31st webinar is free through September 10th.

Math Problem Solving - Mindsets Matter 

Best Practices in Math Instruction: Agree or Disagree? 
At the beginning of the webinar, I'll ask you to evaluate 6 commonly-held beliefs about math instruction, and then I'll share what the research tells us about them. What do you think about each statement below? Do you agree or disagree with these beliefs about math instruction?
  1. Problem solving strategies should be taught before giving students problems to solve. 
  2. Drawing solutions and counting on fingers should only be encouraged for young children and struggling students. 
  3. Students should only use calculators in math after they can perform the computations by hand.
  4. Mistakes are only beneficial when we learn from them.  
  5. Some people were born with a gift for math, and others weren’t. 
  6. The best way to meet the needs of all students is through ability grouping and differentiation. 
If you want to know what the research says about these beliefs, watch the webinar replay! I dug into the best practices related to each of those statements about math instruction.

From Word Problems to Rich Math Tasks
One research finding about how to foster a mathematical mindset is pretty clear. Instead of overloading kids with traditional "word problems," we need to engage them in more in rich math tasks. In the webinar, I went into detail about what that means, but basically a rich math task encourages students to think about math in new ways, finding multiple ways to solve problems, and to discuss their findings with others. Fortunately, it's quite easy to find rich math tasks if you know where to look, and you can also turn traditional word problems into rich math task. Check out the webinar replay for tips about how find or create rich math tasks that are appropriate for your students.


Join Me for a Math Mindsets Webinar Journey!
I'm still learning about how to foster a mathematical mindset, so I consider this webinar to be more of a journey we'll take together. You can board the Math Problem Solving: Mindsets Matter webinar train here; tickets are FREE through September 10th, so hop on and take a seat now!

I'll be your conductor if you decide to take this journey with me, and I'll share what I've learned about growth mindset and math instruction. We'll wrap up our adventure by exploring painless problem solving strategies you can implement right away that will motivate your students to love math, even if you don’t! Who knows? By the end of our journey, you might be a math lover, too!



August 13, 2017

Discover MrOwl, a Free New Tech Tool Teachers Will Love!

Have you discovered MrOwl? It's a free, new tech tool you can use to create a personalized Internet experience based on the topics that are important to you. You can easily build, organize, and customize topic “branches” that you share with friends and family. It's completely free of advertising, too. These features make MrOwl the perfect tool for educators who can use it in the classroom with students and on their own for organizing lesson resources.  You can even use MrOwl to create a free class website!

Using the MrOwl Chrome extension, you can easily save your favorite website links so you know where to find them later. Furthermore, you can upload your own documents and photos to your branches, making it easy to create comprehensive collections of searchable information.

The best part is that MrOwl gets wiser as more people use it. The branches that you build help to shape the MrOwl community “tree,” an ever-growing, searchable collection of web links and resources. These branches are curated by real people in the MrOwl community, not a computer, so they're free of inappropriate content and organized in a way that makes sense. MrOwl is free of advertising, too, so you aren't distracted by annoying pop-ups or sidebar ads.

But MrOwl is more than a safe search engine or a handy bookmarking tool; it's also a unique social media platform that makes it easy to interact with others who share your interests. MrOwl community members can follow other users, message their own followers, and even invite people to collaborate with them on their branches. It truly couldn't be any simpler! Members can also grab, "heart," and share branches created by others.

Explore MrOwl on Your Own
To start exploring MrOwl on your own so you can see how it works, click over to my profile page, @laura_candler, and check out some of the branches I've created. If the page you see doesn't look exactly like the one below, it's probably because you're not logged in. It's easy to create a free MrOwl account, but be sure to choose a user name that you don't mind being public and visible to others. I recommend using your real name if it's available, which is why I signed up with @laura_candler. After you log in, return to my profile page and follow me! Then grab any branches that you like to save them for later and explore MrOwl to find new interests and get inspired!


The MrOwl Backstory
MrOwl is the brainchild of Becky and Arvind Raichur, and their vision dates back almost 20 years to 1999, a time before Google and Pinterest when it was nearly impossible to search the web. Becky and Arvind envisioned making the Internet a better experience for everyone, where it's easy to organize and curate collections of searchable links, documents and more in one convenient place. Their ultimate goal was to create a connected community curated by real people like you, not a computer. The word "crowdsourcing" wasn't coined until 2005, but the concept describes their early vision perfectly!

It wasn't until 2013 that they were able to put together a team to bring MrOwl to life, and it's taken the team several years to build and test the site. During that time, they've added new features that make MrOwl more interactive and easier to personalize. MrOwl began as a web-based platform, but a convenient mobile app was just released so that you can access MrOwl right from your phone or tablet.

Reaching Out to Educators
Now that MrOwl is available to the public, Becky and Arvind are eager to spread the word so that others can benefit from this free tool. They're especially excited about MrOwl's potential for classroom use, which is why they reached out to me. They initially just asked me to review the site and offer feedback about how to make it even more useful for teachers. After I spent time on MrOwl, I realized that it's far more powerful than it appears at first glance, and I knew that I had to share it with others! I was also impressed with Becky and Arvind's sincere desire to make MrOwl even more useful for teachers and more approriate for students. They've already started working on some new features, such as templates teachers can use to create free class websites, and they're open to your feedback and suggestions as well.

Free Webinar: Educators' Guide to MrOwl
To help teachers get started with MrOwl, I recently presented a webinar called Educators' Guide to MrOwl: Intro for Early Adopters. The live webinar is over, but you can register here to watch the free replay. MrOwl is brand new, so if you like exploring new tech tools, you'll love this webinar! MrOwl is a really powerful tool with a lot of cool features for teachers and even more on the way. During the webinar, I'll explain exactly how to get started setting up a profile, creating topic branches, organizing your content, and collaborating with others. I'll even explain how to use it to set up a free class website!  You'll get a sneak peek at new features that will be added soon, and you'll also meet Becky and Arvind Raichur, the founders of MrOwl! Click HERE to register.


Join the MrOwl Educators Facebook Group
I've also created a Facebook group called MrOwl Educators where teachers can learn about new features and get early access to them. Group members can also ask questions and share their ideas for using MrOwl in the classroom. A third function of the Facebook group will be to seek feedback about how to make MrOwl even better for educators, and this information will be shared with Becky and Arvind. If you'd like to join the MrOwl Educators Facebook group, fill out this Google Doc form and follow the directions on that page to request access.

Can't Wait to Get Started?
If you can't wait to get started with MrOwl, jump in right now and register for your free account. It's easy! Remember that your user name will be public and visible on your profile, so you may want to choose your real name to make it easier for others to find you. Set up your profile by uploading a photo, writing a short bio, and adding links to your social media platforms. Then have fun exploring the site and starting to create your own branches.

Be sure to sign up for my upcoming webinar, Educators' Guide to MrOwl: Intro for Early Adopters. Becky, Arvind, and I look forward to connecting with you and sharing ways to use MrOwl in the classroom!




August 6, 2017

Totality Awesome Solar Eclipse: Are you ready?

Are you ready for the upcoming solar eclipse? If not, take a few minutes now to learn about this "totality" awesome event so you can prepare for it properly and enjoy it safely.

On Monday, August 21st, the moon's shadow will pass over the US in a sweeping arc, from Oregon to SC, and if you're lucky enough to be directly in that path, you'll see a total solar eclipse. As the moon passes between the earth and the sun, blocking the sun's light, the sky will darken and temperatures will drop, right in the middle of the day. Eventually, the moon will completely block the sun for 2 or 3 minutes, and all you'll see is the sun's corona, which appears as a faint glow around the edges of the moon.

Sounds amazing, doesn't it? Unfortunately, the path of totality will only be about 70 miles wide, so very few viewers will experience the solar eclipse as dramatically as the picture on the right. Everyone else in the US will see a partial eclipse, even those who are just a few miles away from the path of totality. The farther away you are from that path, the less the moon will block the sun, and the less dramatic the event will be.  From what I've learned, if you're even a few miles outside of that path, the eclipse won't be nearly as spectacular as if you were directly in the path.

But what if you learned that you're less than an hour's drive from the path of totality? Would you make plans to go experience the real deal, or would you be content to see a partial eclipse? How far would you travel to see a total eclipse?

Locate the Closest Place to View a Total Eclipse
Before you answer,  take a minute to find out how far you live from totality. It's really easy when you download the free Totality app from Big Kids Science.

After you open the app and enter your location, you can see the closest place to view a total eclipse, and you'll even be able to get directions to it! You can also learn what the partial eclipse will look like at its peak in your location, how to get to the closest place to see the total eclipse, when the eclipse will begin and end, and much more. The app also includes links to lesson ideas and activities for teaching about the solar eclipse.

Order Your Protective Eye Wear Now 
No matter where you live in the US, if the sky is clear on August 21st,  you'll be able to see a partial eclipse, if not a complete, total eclipse. It's never safe to look at the sun, except for the 2 or 3 minutes of totality when the sun's rays are completely blocked, and only for those who are in the path of the total eclipse. So if you plan to watch the eclipse at all, you'll need protective sunglasses. They are readily available and not very expensive right now, but I guarantee they are going to be much harder to find and more expensive if you wait until the last minute to get them.

I ordered mine from Big Kids Science, the creator of the free Totality app, because I like to support organizations that offer free educational resources like the app. I purchased mine from within the app, but you can also purchase them directly from the Big Kids Science website.

Solar Eclipse 2017 or Bust!
The last total solar eclipse that was visible in the United States happened back in 1970, and it passed right over North Carolina where I live now. Unfortunately, I didn't move to NC until 1973 so I missed it! :-( I lived in New Hampshire at the time and I remember seeing a partial eclipse, but the experience wasn't all that memorable.

That's why I was excited to discover that the path of the 2017 solar eclipse will go through South Carolina which is just a few hours south of where I live now. I learned from the Totality app that even if I stay right where I am, I'll see a very distinct partial eclipse with 96% coverage of the sun. I guess I could be satisfied with 96% totality, but the more I thought about it, the more I realized that this will be my last chance to see a total eclipse, so driving a few hours to see it will be "totally" worth it! I've heard the traffic that day will be insane anywhere within the path of totality, so I booked a hotel room in Orangeburg, SC, which is in the direct path of the moon's shadow. Now my only concern is the weather, and I'm praying for clear skies on August 21st.

How close are you to the line of totality for the 2017 solar eclipse? Are you planning to travel to see it? If so, take plenty of food and water with you, and be sure to start your trip with a full tank of gas. Scope out your viewing location in advance and arrive well before the partial eclipse begins. Finally, remember to bring your totality awesome protective sunglasses!