Open Questions

The ultimate goal of differentiation is to meet the needs of the varied students in a classroom during instruction, but this can seem overwhelming.  One way it can become manageable is if the teacher can create a single question or task that allows students at different stages of mathematical development to benefit and grow. 

This single question is called an Open Question. A question is open when it is framed in such a way that a variety of responses and approaches are possible. 

For example, look that the picture below. Describe what you see by using a mathematical equation and justify your answer.

What equation did you come up with? 

How many equations could you come up with? 

Can you justify all your equations?

Marion Small in her book called, Good Questions, Great Ways to differentiate Mathematics Instruction suggests 5 ways to change a closed question to an open question.

1. Turning the question around

2. Replacing the question with a blank

3. Asking for similarities and differences

4. Asking for a number sentence

5. Changing the question

Open questions can lead to great classroom discussion that can engage all students. So give them a try and share with us your results!

You may enjoy this book by Marion Small. Inside are many examples of open question for grades Pre K through 8.

Classroom Norms for Think Time and Participation

Good teaching is more a 

giving of right questions than 

a giving of right answers.

~Josef Albers

I love this quote because more and more educators, parents and students are realizing the core of mathematics lies in the act of justifying and reasoning. The practice of questioning is one way that we can get students to discuss ideas and justify their reasoning- a necessity our young learners need when they enter today's workforce.

So what questions can we ask students to elicit some discourse? Here are my favorite questions/prompts:

• Tell me more...
• I don't know, what do you think?
• Why?
• Will it always work?

But sometimes, even when I've tried my favorite questions or planned the perfect reflective question, I still sometimes struggle to get all students to participate with each other, especially those that feel like they "can't do math." (Which is NOT true, of course!)

This year, at the Texas ASCD conference, Jackie Walsh, an independent consultant who has two decades of experience working with educators to improve questioning practices, shared some awesome ideas during her presentation.

Have you ever thought about establishing classroom "Norms" for think time AND participation? Here are Jackie's suggestions:

Think Time Norms
1. Use the pause following the asking of a question to think about the question and to come up with your response.
2. Use the pause after your response to think about what you said and add or change it.
3. Use the pause following a classmate's response to compare it to your own. Be ready to agree or disagree and to add to your ideas.

Participation Norms
1. Raise your hand only to ask a question or to comment on another student's response.
2. Listen with respect to other points of view in order to fully understand and learn.
3. Monitor your talk so others can contribute.

Do students know that when you provide "wait time" that their role is to think about the question and come up with a response? Do students understand how to respectfully participate in a discussion or response? I think some of these norms could be helpful in the classroom. In fact, in the book Academic Conversations by Jeff Zwiers he also addresses this very same topic. (This is another excellent resource!)

Lastly, on my quest to learn more about classroom discourse, here is another video I came across from the teaching channel. If you haven't viewed this yet, I promise, it is worth your 3 minutes!



I'm curious...What are your ideas for getting all students participating in math discussions?

Giveaway: Solving for Why Book!

We have reached 100 followers on our blog! In fact, we currently have 103  116 members! Thank you all for supporting Leander ISD Math Instruction.

In honor of this celebration, we would like to giveaway one copy of this book to a Leander ISD educator who teaches math (teachers, special educators, math leaders and principals):

Solving for Why: Understanding, Assessing and Teaching Students Who Struggle with Math 

by John Tapper

To be entered in the giveaway you must:

1. Follow our blog.

2. Comment below why you would like a copy of this book.

The drawing will be next Friday, October 25th at 3:00pm!

Drawing is closed! Congrats to Lela W. at DCE! Thank you to all for participating. We enjoyed your comments.

If you are already reading this book, join us on Twitter with your learning! #LISDSolvingforwhy

Guest Blog: A Principal's Perspective on Number Talks

This week we are proud to introduce our first guest blogger for the 2013-2014 school year, Principal Mark Koller, from Pleasant Hill Elementary! Principal Koller and his staff are working hard to transform math instruction and they know that it begins with action steps and trying a few things different. Let's learn from this principal as he begins his journey with Number Talks...

There are many benefits to being a campus administrator. You get a sweet walkie-talkie, maybe an extra nugget or two in the cafeteria, and most importantly, the joy of working with hundreds of students on a daily basis. I love my job, but as an administrator, I do miss the interaction, academic conversations and relationships built in the classroom setting that thousands of teachers across our district experience each day. Luckily for me, my staff allows me to pop in from time to time and teach.

Recently, I was able to work with my fourth grade team facilitating Number Talks in six different classrooms on six consecutive days. If you’ve read this blog before, you are probably very familiar with the basics of Number Talks. We were fortunate enough to have our math curriculum department on campus this week, and I also had the fortune of hearing from them in my district admin meeting. The point that hit home with me, and what I tried to model in my lessons this week, was the three pronged approach to math:

1: Make Sense of the Math

2: Do the Math

3: Use the Math

According to Cathy L. Seeley, author of Faster Isn’t Smarter, students must have a “conceptual understanding,” while utilizing “facts, skills, and procedures,” when problem solving. (Seeley, 2009) This to me, reiterated the make sense of, do, and use the math approach.  Equipped with this information, I felt ready to get into the classroom and work with the students.

I started my Number Talks journey in Mrs. Lukes’ class. The students and I discussed 27x5. As with every Number Talk, I ask if anyone had a way to solve that problem. Hands went up or really hands went to their chest and they started gesturing to me in a sort of Number Talk sign language that took a second to decipher. Each student held up the number of ways they could solve the problem.

• The first student I called on started to talk to me about friendly numbers and why it’s easier to count in ones, 2’s, 5’s, and 10’s She encouraged me not to look at the problem as 27x5,  but more as 20, 5, and 2 multiplied by 5. This way I could literally count by 20 five times, 5 five times and 2 five times. I was super excited. I could hear Yoda saying, “Conceptual Understanding this one has.” (Star Wars reference)
• A second student made the point that multiplication was repeated addition and I should just add 27+27+27+27+27 to get to our eventually goal of 135. I was pumped.
• A third student said to just multiply the numbers using the traditional algorithm to solve it. When I asked this student to walk me through this, he stumbled on some steps. While participating in a Number Talk all answers are valued and validated. The conversation with the students is the basis of the mini lesson. This particular student was on the right track but just was not sure how to move the numbers around in the algorithm to bring him to ultimate success, and could not explain the reasoning behind it. My advice to him and the student in the second class I worked with that wanted to write out 27 dots, five times and then count up all the dots was similar; When choosing the best strategy it is important to pick one that you understand and will ultimately bring you reasonable and efficient success. I found myself reiterating this point over and over in all six classes: make sure you can make sense of what you are doing first.

When asked how you came up with your strategy, a student’s answer shouldn’t be my teacher showed me. It should be based on the numbers and how they can manipulate their thinking with them. Algorithms are great in some instances. They should be used as a tool for doing the math only after we can make sense of it. Reasonable, efficient strategies are ones in which we are not setting ourselves up for failure before we even start. Putting 27 dots on the paper five times in a row is a recipe for miscounting and frustration. They may start there, but encourage the progression from dots, to tally marks, to numbers, and then finally the friendly numbers that will help them succeed in an efficient manner.

Encourage your students to look for the friendly numbers that the first student I encountered encouraged me to do. Think in numbers that are easy to manipulate and don’t settle for 13 to be 13. Let it be a 10 and a 3 or two fives and three ones.

Bridging the conversations from the Number Talk to the application or the “Use the Math” portion of the classroom is the key for ultimate learning target success and the recipe for cooking up mathematical thinkers. I look forward to revisiting these classrooms and others in the coming weeks and Tweeting out the evidence of great Number Talks and math conversations. You can follow me, @KollerTX, on Twitter.

Problem-Solving Challenge of the Month: September

One of the most critical features of a balanced math classroom is problem solving! Each month this year we are going to post a problem-solving challenge that we encourage you to give your students the opportunity to solve. Every problem that we give this year for the monthly challenge will have some connection to place value. Last year, we had a blog post that touched on this topic. Check it out!

All students must have a solid understanding of the base-ten number system by the time they leave elementary school. So, what does it mean to develop a base-ten understanding? As educators, we must provide students opportunities to explore the relationships of the powers of ten and this is a key component for how students become fluent with operations.

Even in kindergarten we provide opportunities for students to:
-see numbers as tens and ones
-use the structure of our number system to count with understanding
-use the structure to develop operations

So how can we help students to gain a deeper understanding of the base-ten system? You can begin by posing this problem:

This is a measurement division problem type and the "measurement" is ten. We are putting ten markers in a box which is the central organizing number of the base-ten system!

One of the best ways to differentiate a math problem is by giving different number choices. Decide on which numbers would be best for your class. Have students select "Company A, B or C" and start solving!

As students solve, observe how students are thinking and select varying levels of student work to share. Here is an example of some student work:

Gather students together and discuss the similarities and differences between each strategy. This is the fun part! Allow students make conjectures about the math. Ask, "What do notice? How do these strategies build on each other? Do you see any patterns in our solutions?"

After you solved this problem with your students, share a comment below and let us know how it went! Post picture on twitter using #lisdelemmath. We can't wait to learn with you!

Partnering with Parents - How to Support Math at Home?

Tis' the season for Back to School Nights and Parent Orientations.
It is critical for educators to communicate with parents their role in the partnering with the teacher, classroom and school in their child's mathematical journey.  

It's easy for parents to forget that math is more than just addition and subtraction worksheets and memorized facts. It is our responsibility to look for ways to show children how math is such an important part of our everyday lives: cooking and shopping, art and music and computers – it is all math.

Here are some ways parents can help their child connect and practice math in “real life.”

1. Have your child count down the time (weeks, days and/or hours) to a special day or holiday.
2. Have your child measure ingredients for a recipe you are making.
3. Encourage your child to track or graph scores or stats for a favorite sports team.
4. Ask your child to count the change at the grocery store, or to estimate the total cost while you are shopping. Or, with older kids, to help track the family budget.
5. Explain what you’re doing whenever you use a measuring tape, a scale, or a ruler. Ask for your child’s help.

Download

Additionally, Cathy Seeley also has a GREAT message to share with parents from her book Faster Isn't Smarter:  A Math Message to Families

The National Council of Teachers of Mathematics also shares resources that might be helpful to share with parents.   NCTM Family Brochure

 

Whatever you decide is important to share, please make it a point to let families know how important it is for you to Partner with Parents!