Tag Archives: learning

Two Math Routines to Learn About Student Thinking

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Routine 1: Tell Me Everything You Know About ____________

Directions

  1. Choose a word or phrase that is the focus of your first curriculum unit. This could be something like: fractions, addition and subtraction, shapes, data, multiplication, etc. If students are introduced to that concept for the first time during the unit, such as volume in fifth grade, use a term like ‘measurement’ to elicit prior knowledge related to volume.
  2. Write your chosen concept or topic at the top of a piece of chart paper.
  3. Prompt students, “Tell me everything you know about [your chosen topic].”
  4. Give students 1 minute of independent think time and then 1 minute to quickly tell a partner one thing they are going to share with the whole class.
  5. As a whole group, record students’ ideas on the poster as they share.
  6. When they are finished, ask if there are any ideas on the chart paper they have questions about. This is a good opportunity for students to ask clarifying questions of one another, revise their thinking, and agree or disagree with others’ ideas. You do not need to come to a final conclusion on each point of disagreement, especially if it is something they will learn in the unit. Simply just mark that idea with a question mark and revisit it later.
  7. If there is time, you could start another poster with the prompt, “Tell me everything you wonder or have questions about [your chosen topic].” This communicates that sharing things they wonder and asking questions are part of learning. The information you’ll learn about student thinking will be extremely helpful going into the first unit.
  8. As you move through the first unit, refer back to the poster frequently and ask students if they would like to add anything new or revise a previous idea.

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Routine 2: Talking Points

Directions

  1. Arrange students in groups of 3 or 4. 
  2. Print a copy of the talking points for each group. 
  3. As a class, review how each round works. The first time you do this, it might be helpful to also model the process with a fun talking point such as, “A hot dog is a sandwich.”

ROUND 1 – Read the first talking point aloud. Take turns going around the group, with each person saying in turn whether they AGREE, DISAGREE, or are UNSURE about the statement and why. Even if you are unsure, you must state a reason why you are unsure. As each person shares, no one else comments. You are free to change your mind during Round 2 and/or Round 3.

ROUND 2 – Go around the group a second time, with each person saying whether they AGREE, DISAGREE, or are UNSURE about their own statement OR about someone else’s agreement, disagreement, or uncertainty from Round 1. As each person shares, no one else comments. You are free to change your mind again during Round 3.

ROUND 3 – Go around the group a third time to take a tally of AGREE / DISAGREE /UNSURE votes and record that number on your Talking Points sheet. Then, move on to the next talking point. 

Sample Student Handout with Third Grade Talking Points

Talking PointAgreeDisagreeUnsure
Fractions are always less than 1. 
A fraction is a number.
We can locate fractions on a number line. 
Fractions tell us a size. 
One half is always greater than one third.
We can combine fractions.

Sample Math Mindset Prompts

  • Being good at math means being able to do math problems quickly.
  • A person is either good at math or bad at math. 
  • I prefer to work on problems that challenge me rather than ones I find easy.
  • When working in a small group, if one person knows how to solve the problem, they should show the others in their group how to do it. 
  • There is always one best way to do math.
  • Getting a problem wrong in math means you failed. 
  • Drawing a picture is always helpful when doing math. 

Sample Math Content Prompts

  • 5 is the most important number.
  • The number 146 only has 4 tens.
  • Fractions are numbers. 
  • When multiplying, the product is always greater than the factors.
  • Division of fractions is just like division of whole numbers. 
  • The opposite of a number is always a negative number.
  • It is easier to work with decimals than with fractions. 
  • For any equation with one variable, there is one best way to solve for the variable.
  • It is easier to work with degrees than with radians.

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Leveraging Digital Tools for Problem Posing

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I have blogged a few times about problem posing using print materials and lately I’ve become really interested and excited about the potential for digital tools in this work!

If you are new to problem posing, below are a few slides from Jinfa and my NCSM presentation for background – each image is linked to an associated research paper.

What is problem posing?

Many activities can easily be adapted to provide opportunities for problem posing by removing task questions (left) and replacing it with different prompt options (right).

original curriculum activity
problem-posing prompt options

How can digital tools enhance problem-posing experiences?

Being relatively new to both problem posing and digital lessons, I have learned so much trying things out in math classes this year. As always, the more I learn, the more questions/ideas I have. Below are two digital lessons that involve different flavors of problem posing.

Lesson 1: Our Curious Classroom

You can click through the lesson screens to see the full flow, but in a nutshell, students answer questions about themselves and explore different data displays.

After answering the first survey question, we asked students for problems they could answer about their class data and recorded their responses (sorry for the blurry image, I had to screenshot from a video clip:).

The students then worked at their table to answer the questions based on their choice of display.

The lesson continues with more survey questions, data display exploration, and ends with students personalizing their own curioso character (see bottom of post for unrelated, cute idea).

Things I learned:

  1. Student responses can be collected and displayed so quickly with digital which saved us more instructional time for posing and solving problems.
  2. The capability to see data displays dynamically change from one to another enhanced the discussion about which display was most helpful to answer the problems and why.
  3. Students were so motivated to answer questions about themselves, learn about their classmates (audio clip below), and ask and answer questions about their own class, not a fictitious one.
“What did you like about the lesson?”

Things I wonder:

  1. While having the teacher record the questions on the board worked perfectly, I wonder if or how younger students might digitally input their own questions w/o wearing headphones for voice to text or having spelling errors that are challenging for others to interpret? Maybe something like a bank of refrigerator magnets to choose from?
  2. During the lesson, could the teacher input student questions onto cards in the Card Sort in Desmos so they could then sort the problems based on structure before solving?

Lesson 2: Puppy Pile

In this lesson, students generate a class collection of animals, are introduced to scaled bar graphs, and create scaled bar graphs. This one has a different problem-posing structure than the the first lesson which was interesting!

In this lesson, students use the Challenge Creator feature. In order to pose their problem to the class, students create their own set of animals (left) and then select a scale and create a bar graph (right).

After submitting their challenge, students then pick up one another’s problems and solve them.

Things I learned:

  1. Students were extremely motivated to create their own problems and solve the problems of others.
  2. This version of problem posing allowed students to have more control over the situation around which they were formulating problems, which they really enjoyed.
  3. Challenge Creator is an amazing tool for repeated practice that is MUCH more engaging than a worksheet of problems.

Things I wonder:

  1. How could this activity structure support or extend the problem posing experience in Lesson 1?
  2. What other K-5 math concepts would be great candidates for a Challenge Creator problem-posing activity?

Final thoughts

I think problem posing is such an important instructional structure whether done in print, digital, or a hybrid of the two. It is important, however, to also consider the math, student motivation, and amount of time students spend engaging in the problem-posing process when choosing the format we use.

I would love to hear about what you try, learn, and wonder whether you try these lessons or adapt other lessons for problem posing!

Unrelated by Adorable Idea…

After Lesson 1, Katie printed out their personalized Curiosos for the wall;)