How to Recharge Mathematical Thinking

Why do so many students struggle with math word problems? Maybe they just don't know where to begin and get overwhelmed at the thought of tackling math problems. Often students lack experience with different types of problems and the strategies for solving them, so they feel defeated and give up before they get started.

What can we do to help our students overcome their word problem phobias? One strategy that worked for me was to give my students opportunities to talk over how they planned to solve word problems before I let them pick up their pencils to work on them. Not just once or twice, but over and over until they were able to build confidence as problem solvers. At first, some of my students didn't participate actively in those discussions. But eventually they jumped in with their own strategies, and they were so excited when their methods worked!

If you're skeptical, you might be thinking about discussions you've observed in the past. Often one student does all the problem solving, and everyone else writes down his or her answer. But these discussions don't really qualify as cooperative learning because group members are not participating equally.

Recharge & Write for Math Problem Solving (Freebie)
To address this situation, I developed a strategy called Recharge & Write to encourage active participation and provide accountability. The basic concept is that students alternate between team discussion and independent written response. They first discuss each problem as a group, but when it's time to solve the problem and write their answers, they aren't allowed to talk. This strategy ensures that they will become active participants in the problem-solving process rather than letting others do their thinking for them. I recorded this short video to show you how it works. Click here to download the free directions and "recharger" label shown in the video.


Advanced Preparation for Recharge & Write
This strategy is easy to implement, but you'll need to do a little advanced prep the first time you use it. Recharge & Write has two important components: a "Recharger" (pencil holder) for each team and a math problem solving worksheet for every student. Read on to find out how these two components work together to provide structure and accountability.

1. Rechargers (Holder for Pencils)
Each team needs a cup or can (the Recharger) to hold their pencils during the team discussions. When students are ready to write their answers, they take their pencils out of the Recharger and write without talking. The beauty of this method is that it keeps everyone honest and controls the flow of the activity. Pencils In = Talk It Over. Pencils Out = Write Without Talking. Simple!

If your students ask why the pencil holder is called a "recharger," explain that when the pencils are in the holder, your students are recharging their mathematical thinking by discussing how to solve each problem! To make a fun recharger out of a can like the one shown in the photo above, use this free label that's included in the Recharge & Write freebie. Wrap it around a clean can and secure it with tape or glue.

2. Math Problem Solving Worksheets (with Space To Show Work)
The other necessary element is a worksheet that has just three or four word problems and provides plenty of space to solve each problem and to illustrate the answers. It's essential that students show how they solve each problem. You can create your own worksheets, or use math word problem worksheets from the one of the ebooks in the Daily Math Puzzler series. The worksheets are divided into quadrants, and each section has one word problem, a line for the answer, and space to illustrate or explain the solution. Download these free samples from the bottom of the Daily Math Puzzler page.

How to Introduce Recharge & Write
Before you introduce this activity to your students, seat them in teams of three or four and place a Recharger in the center of each team. Give the students on each team a copy of the same problem solving worksheet. (Note: If your students differ greatly in ability, be sure to read my suggestions for differentiating instruction below). Ask each team to choose the first Leader or appoint the Leader yourself. Display the Recharge & Write directions and walk your class through the process, allowing time for discussion and writing. Remind them that they may only discuss the problem when all pencils are in the cup, and they should not solve the problem and reveal the answer in that step. After they pick up their pencils to work out the problem, they may not discuss the problem further unless all pencils go back in the cup.

Management Tip - At first you may want to serve as the Leader and guide the whole class through the activity, stopping to allow time for discussion and writing. As your students are discussing the problems or writing, you can walk around and monitor their progress. Be on the alert for students who try to work ahead on problems before the rest of the team is ready. This is a natural error because most students are not used to this stop-and-start method of cooperative problem solving. Just remind them to follow the directions as described.

Calculator Use
Should you let your students use calculators during this activity? That might depend on whether or not your students will be expected to use them on state tests. If you do allow them to use calculators, be vigilant when requiring them to show HOW they solved each problem, preferably by illustrating the strategy in some way.

To Grade or Not to Grade? That is the Question!
Most cooperative learning activities are just for practice and really shouldn't be graded. In most cases you don't know whether everyone who participated understands the skill being practiced. However, Recharge & Write is a little different as long as you enforce the "no talking while writing" rule. After the discussion stage is over, everyone has to solve the problem independently and show their work, so I think it's fair to grade their work. Let your students know in advance if you plan to grade the assignment, and you may want to use a rubric that includes points for effort and participation.

Differentiating Instruction

If you have students performing on vastly different levels, you can imagine what will happen if you put them together on one team. The students who struggle in math are going to be extremely frustrated, and the advanced students will be bored. This is a recipe for hurt feelings and off-task behavior. To solve this problem, reseat your students for this activity and place them in teams of students with similar ability levels. Give each team a different worksheet based on their needs.

The four leveled ebooks in the Daily Math Puzzler series can make it really easy to differentiate Recharge & Write. The books are leveled from A to D, and the problems range from about 3rd grade to 6th grade. You can preview each ebook to see the problems for yourself, or you can use my free Problem Solving Assessment pack to help you determine the right level for each student.

Beyond Cooperative Learning
Allowing your students to discuss math problems before solving them will definitely recharge their mathematical thinking and help them become more confident problem solvers. There's no doubt that students benefit greatly from hearing how others tackle different types of problems. However, as soon as your students develop a little confidence, it's important to have them solve word problems independently from time to time. Guess what resource can help with this too? :-) You guessed it! The Daily Math Puzzler program is versatile enough to be used for both cooperative learning AND independent problem solving!

More Ways to Use Recharge & Write
Today I shared how to use this strategy with math problem solving, but Recharge & Write is a strategy I frequently used in social studies, science, and health, too. The directions are slightly different so I didn't include them in this post. I'm working on another freebie with those directions, and I'll share it soon. If you want to be notified when I post it, be sure you are following Corkboard Connections on BlogLovin.

I hope this strategy will recharge mathematical thinking in your classroom!

Teaching Kids How to Have REAL Discussions

Do you remember the last time you and your friends had a great discussion? I’ll bet you didn’t take turns around the table with each person speaking for 30 seconds or a minute! Instead, it was probably a lively conversation with everyone listening to each other and responding to everyone's ideas. Although you didn't speak for the same amount of time, everyone was involved and participated actively. If group members disagreed with each other, they were polite and supported their own views with facts and relevant details. Everyone was energized by the discussion and came away with some new perspectives.

Now think about what happens in team discussions at school. One student dominates the discussion while others are too shy to share their own views. To prevent this from happening, we ask them to take turns around the team ... but those discussions don’t feel like real conversations. It’s obvious that team members aren't really listening to each other because they don’t link their ideas to what anyone else has said. Instead, it’s almost as if they’re simply waiting for their turn to talk. Because most kids don’t know how to disagree politely, either they all agree with each other or when they do disagree, someone's feelings are sure to be hurt. Watching these "discussions" is almost painful!

Learning to Link Ideas
As you know from your own discussions, a great conversationalist is someone who really listens to others and who demonstrates this by linking his or her ideas to those of others in the group.

This skill is so important that it's now stated in the Common Core Speaking and Listening Standards for collaborative discussion at almost every grade level. But how do we teach that skill?

One way to link your response to someone else's idea is to use these steps:

1. Name the person who shared the idea to which you are connecting.
2. Mention a key idea, fact, or opinion the other person shared.
3. Clearly state your own question, opinion, or idea.

For example, "Julie, I can see why you might say that Cindy is outgoing, but I thought she was shy because ...." or "Tom, I agree with you about ________, and another detail that supports your point is..."

Introducing the Strategies

When you begin teaching students to have real discussions in which they link their ideas to others, it's best to start with baby steps. Introduce the concept in a whole group setting by posing a question and asking volunteers to come forward and link arms to show how they are connecting their ideas to others. Model the three parts of a linked response described above.

Next, students can create paper chain links to model how speakers often have multiple discussion threads going at the same time. Finally, you can introduce older students to team "discussion webs" where their ideas are interconnected in complex ways.

During last week's Active Engagement Strategies for Success Webinar (Part Two), I explained how to implement several discussion strategies for linking ideas and why we need to teach these skills. To watch the entire webinar, visit the Active Engagement Strategies page on Teaching Resources. Click the play button below to watch the segment about how to foster great discussions.

Discussion Connections Mini Pack

You don't need to purchase anything to start teaching your students how to have real discussions, but the Discussion Connections Mini Pack offers some time-saving resources to make your job a little easier. It's a step-by-step guide for introducing discussion skills in the elementary classroom, and the basic concepts can be applied in middle school and high school classrooms, too. You'll find all the directions and printables needed, including discussion prompts to help students link their ideas. The pages below let you peek inside, or you can click here to preview the entire Discussion Connections Mini Pack.

Just to clarify, there's nothing wrong with having students take turns sharing ideas around the table, especially when they first work in cooperative learning teams. It's a great place to start! The problem comes in when we don't take our students to the next level and teach them how to have REAL discussions.

In order to have meaningful interactions in cooperative learning teams, literatures circles, and even in the lunchroom, kids need to understand that discussion involves LISTENING as well as talking. When we take time to connect our ideas, we show that we are listening to others and considering their viewpoints, rather than waiting for our turn to talk. Taking time to teach discussion strategies at the beginning of the year will reap dividends later, and those benefits will reach far beyond the classroom!

The Core of Effective Discussions

With the attention given to the Common Core Informational Text and Literacy Standards, it's easy to overlook the other ELA standards, especially the Speaking and Listening Standard. But even though this is not a tested area, speaking and listening skills are extremely important. Knowing how to participate actively in a discussion involves the highest level of communication because both speaking and listening skills are required. Often it's through talking over ideas with others that we are able to dig deeply into core concepts and understand them fully.

Unfortunately, oral communication skills don't come naturally to students. We have to teach those skills explicitly and provide opportunities to practice them. Perhaps that's why the very first speaking and listening anchor standard is, "Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively."

Effective discussion is the foundation for all collaborative work, and there are two strategies I use regularly to promote these skills:

• Think-Pair-Share for whole group discussions 
• Talking Sticks for small group discussions

Before I share HOW to use these strategies, let's take a look at WHAT your students might be discussing when they practice collaborative discussions. Fortunately, the Informational Text and Literacy Standards give us the perfect opportunity to engage our students in effective discussions and teach them how to communicate clearly. These standards are rigorous, and in order to fully explore the concepts outlined in the standards, students must discuss them in both a whole group setting and in small cooperative learning groups or guided reading groups. The standards require far more than finding fact and opinion, making predictions, making connections, and many of the skills we have taught previously.

Creating Standards-Based Reading Questions
After examining the K-5 reading standards in detail, it occurred to me that an easy way to meet many of them would be to involve students in standards-based literary discussions. Simply take each standard, convert it into a series of related questions, and then apply those questions to a read-aloud or other shared text. For example, Standard RI.3.2 is, "Determine the main idea of a text; recount the key details and explain how they support the main idea." After you convert that standard into a few related questions, it reads, "What is the main idea presented in this text? How is the main idea supported by specific details?"

You can create these questions yourself, but I’ve done the work for you by creating sets of Common Core Discussion Prompts for each grade level, K-5. Each grade level includes three sets of prompts: Personal Response, Informational Text, and Literature. The prompts are available in both a full sized PowerPoint format to display for the class and a smaller task card format to use in small groups. The questions to display for the class include the specific standard numbers right on each slide. You can purchase these items from my TeachersPayTeachers store.

Using Think-Pair-Share to 
Foster Whole Group Discussions

After creating a set of standards-based questions, the next step is to present them to your class in conjunction with a relevant text. For the question above, you’ll need a short informational text selection that can be read aloud to your students or that they can read in a basal text. If you are using an entire book, limit your read aloud session to just a few pages that have one clear main idea. For example, Nature's Green Umbrella has several pages that describe the rain forest, several pages about why rain forests are endangered, a few pages about rain forest solutions, and so on. After students read the text or listen to you read it, use the Think-Pair-Share strategy to discuss the question as a class. Follow these steps:

1. Think and Write – Present the standards-based questions for discussion, "What is the main idea of the text? What are the key details? How do those details support the main idea?"  Give students a few minutes of individual think time to jot down the main idea and at least 2 key details.
2. Pair and Discuss – Pair students with a partner and ask them to compare their ideas about the main idea and key details. Ask them to discuss how those details support the main idea.
3. Share with the Class – Call on individual students to share what they discussed with their partner as the main idea and supporting details. Before you confirm any responses as being correct, call on at least 3 or 4 students to share their thoughts. Ask if anyone disagrees, and teach them how to disagree politely and support their idea with details. 

Using Talking Sticks to 
Foster Small Group Discussions 

After you introduce each standards-based question in a whole group setting, it’s time to introduce them in small groups. You can do this in small guided reading groups using the Talking Sticks strategy I described in an earlier blog post.

Each team is given a cup with “talking sticks,” or craft sticks, and teach team member is given 2 or 3 sticks. Throughout the discussion, students use the craft sticks to signal that they have something to contribute to the discussion. They give up a stick when they are called upon to speak, and when they run out of sticks they may not speak again until everyone else is out of sticks. This strategy is great for equalizing participation and keeping individual students from dominating the discussion.

I created sets of CCSS Aligned Talking Sticks task cards for grades K - 5 that have the exact same questions as the full-sized discussion prompts. You’ll find complete directions for using the strategy in each Talking Sticks Mini Pack. You can also purchase the full-sized discussion prompts and the Talking Sticks task cards as a CCSS Aligned Reading Discussion Combo.

If state-testing is looming in the near future for your students, standards-based discussions are a terrific way to prepare them for the rigors of those tests. But even if testing is over, or you don’t teach in a school system that has adopted the Common Core, it’s important to teach students how to engage in effective discussions. Both Think-Pair-Share and Talking Sticks are excellent strategies to boost oral communication skills, and they'll take your students to the core of effective discussion.