Wednesday, February 18, 2015

Number Talk

A Brief Background on Number Talks:

Kathy Richardson and Ruth Parker began giving teachers mental math exercises at professional development settings during the 1990s. As these teachers completed more mental math Kathy saw the teachers becoming more proficient. Kathy and Ruth realized that they wanted to develop students' understanding, but they did this best by using concrete models to figure out computation. This idea lead to number talks. 

So...what is a number talk? A number talk is a short daily routine that gives students meaningful practice with computation. Number talks help students develop fluency while solving mental math problems. One great way to introduce a number talk is after a counting circle. In case you haven't heard of a counting circle here are some blogs to check out:

 Sadie Estrella - Counting Circle
 Malke Rosenfeld - First Counting Circle
 John Golden - Sadie's Circles 

I would love to explain in detail what exactly a number talk is but Jo Boaler does a beautiful job (way better than I ever could) in this video, it is worth the watch!

Here are my Top 5 Benefits of Number Talk:

1. Teaches Number Fluency 
This is in my mind the greatest benefit of number talks. The more students are involved in number talks the deeper conceptual understanding they have about numbers. Students will begin to see different fact strategies for addition, subtraction, multiplication, and division the more they practice. They will then use these known facts be able to see things like 6+7=6+6+1 or 6+7=7+7-1. Students show their fluency when they are able to explain why they are doing what they are doing, and also when they know how to solve a problem using different methods. 

2. Number Talks Build Confidence in Students
Once a student has a deeper conceptual understanding of numbers and how they work they will start to solve mental math problems at a faster pace. It might not happen right away, but the more practice a student has the faster they will get during number talks. This gives our students confidence. They can feel that they are becoming more proficient. I know that this confidence will carry over into their mental attitude while solving other math problems. 

3. Students Learn Different Strategies 
Sometimes a student will solve a problem in a way that other students would have never thought of. By sharing these idea in the form of a number talk our students gets to collaborate and may learn a more effective way of solving mental math problems. You may hear students say things like "Oh I never thought of that!" That is one of my favorite sentences! This means that our students are recognizing that other students think differently than them and that they have valuable ideas to share as well. Even the teachers have valuable things to learn from their students. 

4. How to Make a Problem Easier to Solve
Which is the easiest to solve? 
Chances are that students would struggle more when presented with 13-7 versus 10-4 or 12-6, but the awesome part is they all equal 6! During number talks students begin to see that they can change the problem they are working on to make it easier on themselves. If a student gets uncomfortable solving a certain problem they can change that problem into something easier using their fact strategies! One student might struggle trying to solve 46-29 mentally, but once they see that 46-29=50-33 they might have an easier time solving this problem mentally. Its important for students to be able to make mental math easier for themselves. 

5. Teaches Students Communication
How do we expect our students to be able to communicate about mathematics if they never practice? At first students will struggle trying to explain their thinking during a number talk but the more practice they get the more articulate they are and the more thorough they are in their explanations. One of the 8 Mathematical Practices of the Common Core is for students to be able to "Construct Viable Arguments and Critique the Reasoning of Others". This means that students need to be able to communicate about math, using mathematical language. Number talks are a great way to get our students on the track of mathematical communication, which leads to deeper conceptual understand and fluency, look at that its like a cycle!

Last semester I wrote an article about math anxiety and counting circles. I talked about how nervous I felt during counting circles and how I basically dreaded doing them in class. I can honestly say now that I enjoy counting circles. I enjoy them because of how much the number talks have helped me. Over the last two semesters I have deeper understanding of numbers and better number fluency. Counting circles no longer make me so anxious because I have different strategies to solve mental math problems. I will 100% do regular number talks in my future classroom because they will do nothing but help my students in the long run and make them better mathematicians. 

To Flip or Not to Flip

Flipped classrooms are a hot topic in education today. Many teachers believe that they can do more meaningful mathematics when they use technology to support their students' learning. The idea of a flipped classroom is that the students will learn the content, that normally would be taught with a lecture style, outside of the classroom with the use of technology. This then allows the teacher to be able to use class time doing activites that apply the students' knowlege. Normally students will learn the material by using a combination of videos and coinciding worksheets. These worksheets are normally checked and counted as a "homework" grade. Other teachers may use quizzes at the beginning of class to keep their students accountable for watching the videos the night before.

One of the struggles of teaching is that not all students learn at the same speed or in the same way. While some students may succeed in a traditonal classroom setting, other students may fall behind. The flipped classroom model allows students to rewatch the videos multiple times if they are not grasping a concept on the first try. Also by watching the videos before the next class students can come to class with questions, some teachers even put a spot on their guided worksheets for such questions. 

Having students learn the material independently also allows teachers to give students more individual support. Since class time in a flipped classroom is used to do activites, the teacher is then able to walk around the room and get immediate feedback about where their students are as far as understanding the content. Therefore, if a particular student is struggling then their teacher can spend one-on-one time addressing their questions.

In the Februrary 2014 issue of Mathematics Teacher there was an article about flipped classrooms. Two teachers, Amanda Moore a 7th grade math teacher from Battle Creek, MI and Matthew Gillett an 8th grade math teacher from Armada, MI, observed the effects of flipping their classrooms. Both teachers saw homework (watching instructional videos and completing guided notes) completion rate rise, with one class even increasing by 19%. After doing a unit of flipped instruction both teachers agreeded that by flipping their classrooms student engagement increased in class and they also said they had more time to do meaningful mathematics. The homework completion rate indicated that more students were doing mathematical work outside of school, and students were also engaging in more problem solving in class that previously was provided through homework. 

The last two semesters I have volunteered in Tara Maynard's 8th grade math classes in Zeeland Public Schools. Mrs. Maynard uses a flipped instruction model in her classroom, so I have been able to see the benefits of flipping first hand. Mrs. Maynard uses videos that she makes (with her own voice using an app called ShowMe) for her students' instruction. The students in Mrs. Maynard's class can access these videos without the use of internet at home through their iBooks app on their iPads (Zeeland Public Schools are 1:1). Mrs. Maynard also provides the students with a note packet to complete while they watch the videos. 

Here is what Mrs. Maynard says are the benefits of flipped classrooms:
- She gets to have conversations with everyone of her students everyday
-Truly know what the students understand and what they haven't yet grasped
-There is more time to do explorations, activites, demonstrations, labs, and deeper questions
-Students are able to move at their own pace and learn with their own style
-Supports anywhere anytime learning
-Parents can't give the excuse of "I can't help"

As with everything in life there are also some negatives to flipped classrooms as well. Here are some of the things Mrs. Maynard says she struggles with:
-Time (creating videos, creating activities etc.)
-Still giving paper and pencil assessments
-If its just a video and a worksheet it is not flipped instruction
-Videos can be done wrong (bad lecture, too long, boring, etc.)
-Students still come to class unprepared and waste time

Here is a video of a typical day in Mrs. Maynards flipped classroom.

Mrs. Maynard also asked her students what they thought of learning in a flipped classroom, here are their thoughts.

Almost all of the teachers who have flipped classrooms can agree that students are able to engage more in the mathematics they are learning. While flipped classrooms might have some downfalls I believe the positives outweigh the negatives. I would love to some day use a flipped model for my own classroom. I think that flipped instruction can provide so many learning opportunities for students and isn't that why we are teaching to begin with?