Do Screencasts Have a Place in the Math Classroom?

Last November, I wrote a short blog post titled, Screencasts of Student Math Thinking. In this post, I also included a link to a glog I created containing four screencasts that were created by grade 6 students explaining their group’s multiplication strategies after an initial multiplication lesson. Since that post, there has been a lot of attention around the world on Kahn Academy where students learn from concepts and strategies from videos (screencasts).

I love the idea of screencasting and I think what Kahn Academy is attempting to do is pretty cool. However, I love screencasts even more when they are created by students. When students create math screencasts it enhances their metacognition. It forces them to think about their math thinking not once but multiple times since they can play back their video, watch and listen to themselves explain their strategy or solution. They can edit and record multiple times until they feel that their screencast is appropriate for their classmates to view. The rest of the class can also benefit from screencasts because they can be exposed to different solutions and strategies to the same problem. In addition, the screencasts are more engaging by virtue of them being created by students and using student language. Also, with websites like Screencast.com screencasts are not limited to the hard drive of a single classroom computer but can be accessed via web link from any computer with an internet connection. This would allow students and their parents/guardians to view them from home.

I truly believe in the benefits of screencasting for students in the math classroom. For the past year, I have been religiously promoting it in my school board as a great tool to enhance student metacognition and math communication. Many teachers seem to like the idea of it but I haven’t really seen it fully implemented in classroom. I’ve mainly seen teachers create their own screencasts similar to Kahn Academy and no disrespect to Khan Academy or to teachers but I don’t find teacher/adult generated screencasts very interesting or engaging. I would argue that students prefer to create the screencasts themselves and watch other student created screencasts. So I ask the question Why? Why isn’t screencasting being implemented in the math classroom? Is it too difficult? Too time-consuming?

I’ve embedded the glog that I created mentioned earlier of student created screencasts of their multiplication strategies below.

I would love to know your thoughts on screencasting and how you would implement it in your classroom.

Investigating Arrays Using Bitstrips

I created another interactive comic using Bitstrips that would allow students to investigate arrays and multiplication. In this activity, students help Mr. Ro arrange desks into rows and columns for the first day of school (I know, I know, very teacher-directed seating arrangement) by clicking and dragging desks and into their desired position. The comic problem is open-ended to allow students to create arrays with 12 desks all the way up to 24 desks and to create a variety of arrays for the same number of desks. I have shared this activity in http://bitstripsforschools.com and I would love to get feedback on how this activity goes if you try it with your class.

Using Bitstrips To Create Interactive Comic Math Problems

Recently, I have been working with staff on integrating Bitstrips For Schools into their classrooms. Most of the ideas that were discussed involved using Bitstrips for literacy, social studies, history, health, and even science. However, math never really entered the discussion. So I searched the shared math activities that were posted by other teachers on the Bitstrips For Schools website and only found a total of eight activities. All of these activities consisted of instructions for students to create their own comics. Here is an example of a shared activity that was posted:

Grades: 6-8, Subjects: Mathematics

Create a 3 panel strip to explain how to calculate the area of a triangle and/or parallelogram.

This particular application of Bitstrips is more of an assignment which focuses on students creating a product based on a set task. However, I thought that this program could also be used to create comics based on math word problems. In addition, these comics could be interactive as well due to a feature in Bitstrips that allows students to take an existing comic, ‘re-mix’ it, and save it as a separate comic.

The following is a primary algebra word problem:

Mr. Ro gave a handful of jelly beans to Jonah and to Sam. When they counted them Jonah had 3 red and 2 green and Sam had 5 red and 4 green. They realized one of them had more than the other. What could they do to make sure each had the same number of jelly beans? Justify your answer.

I took this word problem and turned it into the comic below:

In bitstripsforschools.com, I could share this comic as an activity and assign it to my class so that when they log in it would show up in their ‘Activities’ section. The students would then ‘re-mix’ the comic and rearrange the jelly beans, type their justifications in the caption boxes, and save it as their own comic. Teachers and students could also provide feedback on each others comics via the commenting feature. I could see students creating their own interactive math comic problems as well and sharing with the rest of the class to solve.

I would love to hear your thoughts on this idea. I have shared this activity in the Bitstrips For School shared activity section for teachers. Please try it out and let me know how it works out for you.

My Memories of Memorization in Math Class

When I reflect back on my experiences as a student in the math classroom, flashbacks of constant memorization fill my mind. As a primary ELL (English Language Learner), I struggled to retain math concepts from grade to grade and became very anxious during math class. I became a silent student that would rarely participate and quickly learned that if I stayed silent long enough, teachers would eventually give up and stop asking me math questions. However, whatever I lacked in comprehension, I made up for in effort and memorization.

I found a way to cope in the math classroom and realized that if I memorized hard enough and followed the steps demonstrated by my teacher, I would be able to do the math. Sure enough, as I approached the junior grades, I would show up to school in September and would still know my “multiplication facts”. I remembered to ‘carry’ the number when adding, ‘borrowing’ from number to the left when subtracting, and writing a zero when multiplying multi-digit numbers. I didn’t know why I had to carry or borrow or write a zero but it didn’t matter because I could do the math. That just drove me to memorize even more and found myself studying hours in preparation for math unit tests. I eventually  evolved into a master of memorization and memorized anything that I couldn’t understand (cross multiplication, dividing fractions, integer operations, area formulas etc). By the time I reached the intermediate grades, I was getting A’s in math and was considered a great math student by my teachers. I thought I was a pretty darn good math student too. However, my perception of math at the time may have been a bit skewed. I thought math was all about studying hard, memorizing the facts, procedures, and formulas. In grades nine and ten, I was on top of the math world and I equated success in math to achieving math marks in the 90’s. By that time, I had mastered the art of deciphering the high school math textbook. If there was a word problem that I was confused with, I would just find the similar sample problem in the textbook with the different numbers or I would look to the answer key at the back of the textbook, find the solution to the problem and try a variety of procedures or formulas hoping that one of them would eventually lead to the correct answer. I knew how to play the game and was I winning… until I reached senior math.

As I was introduced to the world of trigonometry, calculus, derivatives, vectors, logarithms, I could feel the old but familiar sense of anxiety that I experienced as a primary student slowly creeping back into my mind and eating away at my confidence. I became desperate when my A average fell to a C average and did the only thing I knew how, I memorized harder, pulled all nighters and took summer school. I was still able to graduate from secondary school with an A average with great effort and memorization but as I remember and reflect on my entire math education I realized that I wasn’t really “doing” math, I was “memorizing” math.

I’m not trying to imply that I never learned or understood the math that I was taught. I’m saying that the way I was taught math and learned math was very inefficient. My perception of math was repeating and applying standard algorithms and formulas that I never really understood. I was never asked to try and solve a problem using my own invented algorithms. I was never exposed to mental math strategies for the basic operations. I never used tools like the open number line or an array to add or multiply. Problem solving wasn’t embedded in the curriculum when I learned math but rather a unit that was also taught very procedurally. Math solutions were expected to look identical to the teacher examples and marks were deducted for missing a step or forgetting an equal sign. It took me a long time to realize and accept the fact that my perception of math was false and that I was a product of procedural teaching and it was a hard pill to swallow. Memorizing is not a mathematical process and not an ideal way to acquire an understanding of math concepts and skills. Math in the classroom is about problem solving, reasoning and proving, reflecting, selecting a variety of tools and strategies, making connections, representing , and communicating.

Opening up Questions in the Math Classroom

As a math teacher, I often became frustrated when I gave a math problem to my students only to have a small percentage of the whole class be able to answer the question correctly. Naturally, many of my students became frustrated too. Consider the following problem:

The word problem above is a very specific problem that only has one answer. The fact that there is only one answer is not a serious issue for me or for the students that need to solve it. The issue with a problem like this is the fact that there is only one way to answer it.

This is a very specific problem that requires a very specific solution. If I gave this problem at the beginning of a grade 6 transformational geometry unit or TLCP cycle (Teaching Learning Critical Pathway) there is a good chance that only a handful of students would be able to solve it correctly. This is the kind of problem that I would give at the end of the unit or TLCP cycle since it is a really good assessment OF learning type of problem. Then it should come as no surprise that this problem was taken from the 2008 EQAO math assessment.

But what if I wanted to use this problem to begin my transformational geometry unit? Well, maybe not in its current form but what if I could “open up” the problem so that it wasn’t so narrow and specific and that a lot more students could solve it. Consider the same problem but with some modifications:

This is an example of opening up a very specific math problem. This open problem has more entry points for students than the previous problem since students have a choice in how they can move and manipulate the mat. Open questions are questions that have more than one answer and are great for differentiating instruction in the math classroom. Open questions allow students to solve problems based on where they are at in their math development.

I actually used the “open” gym mat question last year when I helped a grade 6 teacher introduce her transformational geometry unit. At first, the teacher was hesitant. This approach was drastically different from how she usually introduced the unit. In years past, she would introduce each transformation in isolation. First, a note on translations. Second, examples and demonstrations of translations. Third, practice problems involving translations. The three-step process would be repeated for rotations and reflections (This is also how I used to teach math). Therefore, the notion of giving an open problem to her students that allowed them the opportunity to investigate and use any transformation without defining, modeling or practicing them was pretty daunting. However, the results were very eye-opening and informed the teacher’s next steps for the next few lessons. Here are a couple of the student solutions:

All of the students in the class participated and solved the problem in small groups. As you can see from the gallery, there was a range of solutions from the class that brought up some really good discussion during the reflect and connect portion of the lesson where groups were able to explain their solutions to the class and answer any questions about their transformations. Some topics/questions that were discussed were:

  • efficiency in transformations.
  • What is the most efficient/fastest way to get the mat to the desired position?
  • What’s the purpose of the dotted line AB?
  • points of rotation.
  • Can an object/shape have more than one point of rotation?

This rich discussion was able to occur because of the openness of the question and the fact that students had the freedom to investigate and use their own math thinking to come up with a solution. It was also very powerful for the students to see that none of the groups came up with the same solution to the problem. The range of students’ solutions also allowed the me and teacher to determine appropriate action for the next couple of lessons.

For more information on differentiating math content using open and parallel questions please read the following article. (A very good read!)

Online Gallery Walk Using Lino It

In one of my previous posts about the 3 part problem based lesson, I referred to the third part (reflect and connect) as the most important part of the math lesson since the learning comes from the student work. Students are given the opportunity to explain their math thinking, pose questions, defend their ideas, and make connections with other solutions. The teacher is the facilitator of the discussion as well as a participant. The learning comes from the math community.

The following article describes three approaches to the Reflect and Connect: 1)Math Congress, 2) Bansho, and 3) Gallery Walk.

In this post, I wanted to focus on the gallery walk because to be honest, this is an approach that I don’t use very often when consolidating a math lesson. This is an approach that requires a lot of movement of students in the classroom and could possibly take some time and good management skills to facilitate. In most gallery walks, student solutions are posted around the classroom, and students circulate with sticky notes writing down questions and comments and placing it on the solutions. The idea is for students to read the comments and questions on the stickies about their own group’s solutions and use that feedback to help them prepare the explanations of their work to the class. Problems can arise if students aren’t given enough “wait” time to think of questions or comments to write down on their sticky notes. This can result in comments like, “You spelled multiply wrong.” or “I like how you used the colour red to write your solution.” The goal is to promote higher order thinking and questioning but if students aren’t familiar with a gallery walk or need more time to reflect on the student solutions then perhaps an online gallery walk could be a worthwhile alternative.

Lino it is a great web application that provides you with an online canvas and allows you to post online stickies, pictures, videos, and attachments. You can also share your online canvas with others by sharing its URL. Sharing the URL would allow others to post stickies as well. You can probably see how Lino it could be used to conduct an online gallery walk. To give you an idea of what it could look like, I inserted an screenshot of an online canvas with pictures of four multiplication solutions and stickies with questions and comments posted around them.

The comments/questions were generated by a team of math facilitators when I shared the link with them, which should also give you a good idea of how Lino it could be used for teacher moderation of student work.

By using an online gallery walk, students could post their comments/questions in class or at home and have time to reflect on student work and pose thoughtful questions and comments. Groups could review the feedback the next day and prepare the presentation of their solution to the class.

I would love to hear your thoughts about this alternative approach to communicating in the classroom.

A Closer Look at the Three Part Problem Based Lesson

John Van deWalle, Cathy Fosnot, Marian Small, and Marilyn burns are all key researchers when it comes to mathematics in education. According to these researchers, an ideal math lesson consists of three parts. The HWDSB math facilitation team refers to the three parts as: 1) Getting Started 2) Working On It 3) Reflect and Connect.

Let’s just say we are going to teach a grade 5/6 initial three part problem based lesson on multiplication and the goal of this lesson is simply to see what multiplication strategies students are bringing to the table. The “Getting Started” part of the lesson would involve some sort of activation of students’ prior knowledge related to multiplication (simple problem). During the “Working On It” part of the lesson, the following problem could be presented to the class.

29 students are going on a field trip to a museum. The field trip will cost $20 per student. How much will it cost for 29 students to go on the field trip?

This is an example of an open routed question. There is only one answer but there are multiple strategies to get the answer. Therefore, we ask the students to solve the problem in groups and in more than one way. The first strategy will come naturally for some students however, the second strategy may be more difficult to come up with. Again, the goal of the lesson is to see all the multiplication strategies that the students will use solve the problem. As the students “work on it” we would circulate around the classroom asking questions about students’ strategies, guiding students through the process, and allowing mistakes to occur (these will be addressed during the “reflect and connect”). It is also important to note that not every group needs to be finished before moving on to the “reflect and connect”. Sometimes incomplete solutions provide good starting points for classroom discussion.

The third part of the math lesson is the most important part of the lesson but often the part that gets left out by teachers. It is also considered by many teachers as the most difficult part of the math lesson to facilitate. The “reflect and connect” is when the learning of the math concepts really occurs because the learning comes from the student work. This is the part of the lesson where students are given an opportunity to explain their strategies and solutions and where teachers are given an opportunity to focus on key strategies and concepts by guiding a math discussion through strategic questioning. This math discussion is very important because the conversation is less teacher centred and more student centred. Students ask each other questions about their solutions, make connections between their solutions, and defend their math solutions. The goal of the “reflect and connect” is to create the culture of a math community that allows students to take risks and where mistakes are considered to be opportunities for new learning. Ideally, this is what the “reflect and connect” should and could be like however, it takes time to get there. Students need time to learn how to ask appropriate questions, give constructive feedback, and receive constructive feedback. Teachers need time to learn how to ask probing and guiding questions and look for connections between student work.

There are a few ways to conduct a “reflect and connect”. The following article titled, Communication in the Mathematics Classroom explains three different approaches of math communication that can be implemented during a “reflect and connect”:  1) Gallery Walk, 2) Math Congress, and 3) Bansho.

My next post will focus on the gallery walk and a possible way to enhance math communication via Lino it using the following student solutions:

This slideshow requires JavaScript.