Flipping the Classroom? SOLD!

Credits to Jackie Gerstein, Ed.D.

I love my job ~ educating the children of our future! There’s nothing better than having the opportunity to develop creative lessons and activities that I believe are best for a child’s learning while listening to them discuss new ideas/thoughts and watching their eyes light up when they finally ‘get’ the concept!

I’m always trying to improve what I do in the classroom to better meet the needs of my students. And although I’ve blogged about the idea of “flipped classrooms”, and have even flipped a few lessons here and there, I’ve now gone full force with it. We’ve just finished our second full ‘flipped’ unit and I hope to share some of the things I’ve learned along the way.

I’ve got to admit that it was a little scary at first – letting go of the control and placing it in the students hands. And to be honest, they struggled at first too. I am an extremely organized and well planned teacher, thus had the entire unit outlined and prepared. As a teacher of blocked classes, I provided this simple outline to the students so that they would understand the new process and expectations:

Day 1

Day 2

Day 3

Day 4

Day 5

Lesson Objective(s)

Finish Previous Unit


Apply divisibility rules in order to identify a whole number’s factors and write whole numbers as the product of prime factors


Students will find the greatest common factor of two or more numbers

Students will write equivalent fractions

What’s Happening in Class?

Return summative test; students correct mistakes and complete reflections

Teacher has prepared a quick 5-question check for the start of class. Students then break into groups: a focused learning group or an independent learning group (depending on their individual needs). The independent learning group is free to start working through their problem sets. The focused learning group works with the teacher to receive more review. This typically takes the form of an interactive Smart Notebook lesson. These students then also have class time to work on the problem sets.

Teacher has prepared a quick 5-question check for the start of class. Students then break into groups: a focused learning group or an independent learning group (depending on their individual needs). The independent learning group is free to start working through their problem sets. The focused learning group works with the teacher to receive more review. This typically takes the form of an interactive Smart Notebook lesson. These students then also have class time to work on the problem sets.


Students finish corrections and reflections; get parent signatures

Students watch instructional videos, do online practice problems, and optional activities for our next lesson (posted on the HW page). Students complete reflection questions in google form (link available on HW page) so teacher can plan lesson appropriately.

Students finish the problem sets and correct them.  They then complete the Problem Sets Reflection Sheet (google form; linked to our HW page).

Students watch instructional videos, do online practice problems, and optional activities for our next lesson (posted on the HW page). Students complete questions in google form (link available on HW page) so teacher can plan lesson appropriately.

Students finish the problem sets and correct them.  They then complete the Problem Sets Reflection Sheet (google form; linked to our HW page).

So, in order to plan accordingly, I started by looking at all of the learning goals for the unit. From there, I began searching for online, instructional videos that were aligned with each learning goal. I tended to use videos from Khan Academy and BrainPop most often; these are perfect for grade 6 math. If I couldn’t find a video that connected, then I would make my own.

Next, I knew I wanted to collect feedback from the students regarding their understanding of the skills/concepts before they came to class so that I could plan appropriately … so for every set of videos, I created a set of reflection questions that they needed to respond to while, or after, watching the videos.

NOTE: I started by essentially asking the students the same questions on every video reflection sheet, but realized that they learned to respond with what I wanted to hear. So, I’ve altered my approach and now create different questions each time, including some that ask them to compare a previous topic to a new one and always one that asks them for questions that they might still have regarding the lesson objective. Most of the questions are posed to get the students to think, not just reverberate what they heard in a video. This has been a positive change.

When the students come into class, I have a sense of what I still need to review and can actually post their misconceptions and/or questions up on the screen while addressing them (I can hide the student’s name since the reflection is done in a google form). I’ve attached a sample reflection form, completed by the students. You can see the highlighting that I’ve done in the spreadsheet – these areas represent things that I want to bring up in class. I actually project this for all students to see so we can discuss the questions or responses together.

NOTE: I didn’t post the students’ responses initially, but found that when I did, everyone saw what the others were writing and this encouraged them to put more thought into their responses.

Following our discussion regarding their responses and questions, I project 5 basic questions that the students should be able to respond to in less than 7 minutes. We grade them together and this becomes the design of that class period. For any student who answers them all correct, they are considered independent learners. They gather with other students and begin to work through a set of assigned problems. For any student who misses 3 or more, they must work in a small learning group with me. We use an interactive Smart Notebook that I have prepared. We spend the 10 minutes discussing the concept, creating connections to real life, and finally getting the students up to the board, manipulating various things to try and understand the math better. At the end of our short lesson, they are now independent learners. And finally, for those students who missed 1 or 2 on the 5-question check, they need to do some reflection and determine the best place for them to work.

NOTE: At the start of flipping my class, I had not incorporated the 5-Question Checks, but have found that the students are held more accountable for ‘trying’ the understand the concepts before class with them in place.

Once the students are all working in their independent learning groups, I wander the room. I constantly remind the students that only mathematical conversations should be taking place, and it’s great to hear them. The environment in the classroom is one of open questioning, helping one another, conferencing with one another (including me), and lots of mathematical conversations.

With this model, the students are learning to become responsible individuals for their own learning, advocates for themselves when they don’t understand something, reflective learners, motivated to do more if needed, and resourceful.

This is what I believe powerful learning is all about!


From Understanding to True Application in Math

(This is somewhat a continuation of my previous post titled “Getting Students to Think and Understand Mathematically”)

As teachers, how do we get students to show their true understanding of a mathematical concept without just solving a math problem or explaining the steps? I spend a lot of time pondering this question and would love to get to this point, on a daily basis, in my classroom. What a shift in paradigm that would be … imagine it … a math class that didn’t focus on just skills and solving paper/pencil math problems! One, that instead, requires students to think and stretch their minds and produce work that is connected to real life.

At the start of my “Statistics and Graphing” unit in grade 6 math this year, I asked students to identify similarities and differences in a variety of graphs that they had found. They shared their findings with the class and actually described the different graphs much better than I would have imagined. Immediately I knew that the entire introduction to the unit was a powerful one because the students had done the thinking, connecting, and verbalizing without much guidance from me. This inspired me to continue along this same path … so the next day the students came into class, they saw six different questions on the board, ranging from “How many siblings do you have?” to “What’s your favorite pizza?” to “What month were you born?”. They were set up so that the data collection was done through tally marks.

As we began to enter the data into a spreadsheet, the students needed to figure out the best way to record it. Most students chose a t-table demonstrating the frequency as a whole number. A few students actually figured out how to enter the data as tally marks (I am still not sure how they did that :)). Once again, I didn’t guide them much other than to explain what we use spreadsheets for and what purpose a spreadsheet cell serves. I wandered around the room for the next 20 or so minutes listening to the little fingers tapping the keys of the laptops, and an occasional student asking someone else for help. Once all the data was entered, we were ready to move onto the application (‘fun’) part of the unit.

Students would come in each day with a new task written on the board. For example, they might see these questions:

Guiding Questions:
1) Look at the different data sets. Which ones could be used to create a simple bar graph? Why?
2) Which ones could be used to create a circle graph? Why?

Students would be required to answer these questions on their own, based on the intro lesson and class discussions that had led up to this point. Once they developed an answer and the mathematical reasoning to support it, we would do the task at hand. Of course I needed to teach the students how to graph using ‘Numbers’ since this entire program was new (and I also created an instructional video for those students who needed to view it a second time) YouTube Preview Image~ but once they got the hang of it, they were able to do most of the graphs on their own. As they would produce the graphs, I would slowly walk around the room and ask open-ended questions like “so what does your graph show the reader?” or “is that the best choice of graph to display the data from your data table? how do you know?”. I would hear students say “Ms. Nave, this doesn’t look right” or “Oops, I didn’t chose the correct graph”. I love the moments when students are able to identify their own mistakes and work through them! Eventually, each student completed the process of making their graphs. Once each graph was completed, they had some “higher-level thinking questions” to respond to based on the graph they completed. (See the attached thought-provoking questions) The unit continued in this manner until all data was graphed and all graphs that the students needed to learn, based on our standards and benchmarks, were made.

We then moved onto the idea of statistics (mean, median, and mode) … and continued to use the laptops to teach and practice these mathematical concepts. We taught our students how to write formulas and sort data within the Numbers program. We provided our students with data that we had collected from the students since the beginning of the year (diagnostic test results, prediction of a minute, MAP test scores). This made it exciting for the students because it was real data! See the attached activities, used within Numbers for Mac.

After weeks of practice, not only in Mac Numbers, but also with stretching their thinking in a different way, the students were ready to show us what they learned and understood about statistics and graphing … so the assessment was created in Numbers. And you guessed it – they completed the test on their computers and submitted it to us digitally. I have included a completed test here: Completed Student Assessment. The true test came about 4 weeks ago when a grade 5 teacher asked if my 6th grade students could teach her students how to graph within Numbers. My first reaction was … yeah, that sounds great … but as I thought it about more, I wondered if I was going to have to reteach everything again. I decided to spend the next math class doing a quick check-in to see what they remembered. I asked my students to open up their laptops and go into Numbers. (Yeah, of course I heard a few grumbles, but who doesn’t when you teach sixth grade?) I posted some make believe test scores on the screen and asked the students to create the best graph to display the data. I would say that about 80% of my students could complete this task individually, and then they were ready and willing to help others in the class. I was definitely pleased with that outcome 5 months after we completed the graphing unit. When they heard that they were going to get to teach this to the 5th graders, they actually cheered!

Getting Students to Think and Understand Mathematically

Climbing the ladder to higher understanding … this is something both me and my students are constantly working on to improve!
Attribution Some rights reserved by degreezero2000

The longer I teach, the more I philosophize about what good teaching truly means to me. I am passionate about teaching students to think and actually show their understanding. I don’t just want the students to regurgitate some math fact or memorize the steps to solving a problem; I want them to be critical thinkers and be able to explain their thoughts mathematically.

For the past four years, I have worked in 1 to 1 international schools, therefore have taken advantage of both Microsoft Excel and Pages (iWorks) during the statistics/graphing unit. The typical approach I’ve adopted when using these programs is to teach the step-by-step process for how to graph data that’s been provided, or possibly collected by the students. I have been known to do this every day, for several days, until we have learned how to make a line graph, bar graph, circle graph, pictograph, etc. Then, we might answer a few questions about their graphs to check for understanding. But does this process truly check for understanding?

This year, I wanted to approach the teaching of this unit differently. I wanted the students to be critical thinkers and be a part of the learning process.

We started the unit with a pile of magazines and newspapers, and my only direction was to cut out anything that looked like a graph (I didn’t clarify beyond those directions). They worked at tables consisting of 4 people, and each group found at least 30 graphs. From there, I asked them to try and classify the graphs that their small group cut out. Once again, I didn’t give them any further instructions. When every group was finished with that exercise, they presented the classification system they used to the class. We identified similarities and differences amongst the groups. Now for the hard part … we needed to come up with a classification system for the class and reorganize our graphs. Well, it wasn’t really that hard – the students sorted it out in less than 10 minutes (bar graphs, circle graphs, line graphs, pictographs, frequency tables). Each similar group of graphs were then glued on a large poster board in preparation for the next activity.

During the next portion of this activity, the students rotated from one group to the next, making observations about the graphs they saw glued on the poster boards. They were asked to find the similarities, differences, and anything else that they observed within a common group of graphs. They each had their own editable PDF document (that I created but made accessible to the students) with a chart to record their observations. They rotated around all five groups and then had an opportunity to share their observations with a small group of 4. It was fascinating listening to the mathematical language being used amongst the students. After all members shared, they had one last step to complete as a group: to go back and review their lists, and highlight the key points (the ones they felt were the most important) that they would want to share with the class. This step required them to reflect on what they had written, really question the validity of each point, and discuss which points were the best mathematically. As a class, each group presented their findings and this is what they came up with:

click to enlarge



The mathematical connections and language that the sixth graders used to describe each type of graph truly amazed me! This piece was the connection to everything the students learned in the unit. And this year, compared to all others, the students had a much better understanding of graphs because they were part of the learning process.



Teaching and Learning in the 21st Century

What does it truly mean to teach/learn in the 21st century?

Education has had a complete makeover since I was a student … and even as a teacher, I still feel that I’m a learner in my own classroom. Everyday, I learn something new, usually related to technology. And often times, I am learning the skill from one of my students. I have learned that I must be open-minded, flexible, and approach teaching as a two-way street in my classroom.

As educators, we know that our goal is to prepare our students to be functional citizens in the global world. We do this through teaching academic skills, as well as life skills. We know that our students must be able to ‘decode, comprehend, interpret, and develop a new understanding of the various materials they read. We also know that we must develop independent learners who can gain the necessary skills to survive and succeed. Through the acquisition of these skills, we need to prepare our students to use the skills, understand their own responsibilities, and take time to self-assess – the key ingredients to thriving in a complex environment’ (adapted from the AASL standards). These standards are written in a fashion that leaves them somewhat open-ended.

In looking at the NET standards, the underlying themes are that students will:

  • Demonstrate creativity and innovation
  • Communicate and collaborate
  • Conduct research and use information
  • Think critically, solve problems, and make decisions
  • Use technology effectively and productively

These two documents truly overlap one another. The bottom line is that when we put all of it together, we should be utilizing a variety of resources (digital, visual, textual, and technological) to create students who are competent with multiple literacies. In putting this into practice with my grade 6 students, I attempt to teach by utilizing the various literacies. I start by preparing an interactive, digital lesson (using Smart Notebooks) every day. The students are active participants and learners throughout the lesson. I provide the students with a prepared, paper copy note page where they must record notes from the lesson (i.e. vocabulary, practice problems, real life connections). At times, I ask students to watch a BrainPop video on their own, complete the review quiz, and send me their results; or we may even watch a video together as a class. (In fact, here’s such a fantastic one that I had so many students wanting the link so that they could go home and watch it again.) YouTube Preview Image  And this link, somewhat related, is a great one too! Other times, I may ask the students to log into a simulation or game website to practice math problems. I teach my students how to properly read a math textbook, find key words and/or ideas, and choose problems that relate to our learning objectives, while also challenging them at an appropriate level. My students are asked to log how much time they spend on homework, whether or not they choose problems that related to our learning objectives for the day, and if they were properly challenged from their homework. At the conclusion of each unit, the students reflect on their learning from the unit and share their reflection with me.

I strongly believe that 6th grade students (aged 11 & 12) still require a lot of guidance, but my hopes from all of this is that they will learn to function independently by the time they are in grade 7.

Student-Created MathCasts

This is the second year that I have asked my grade 6 students to create a MathCast based on one specific topic that they have learned during the year. It is my favorite project from the year because it’s amazing to watch and listen to these 11 & 12 year old students “teaching”.My plan is to create a large database of student-created math instructional videos that can be used year after year. This could potentially lead me to running an entirely ‘flipped’ classroom, with all lessons being taught by other 6th grade students. How cool would that be?!

*For more info on ‘flipped classrooms’, check out this blog post. In fact, a flipped classroom book will be coming out this year and seems to be the new way of teaching — a great way to get “increased student interaction.”

For the Math Cast projects, each student chooses a topic or skill that they have learned throughout the year in Math 6. They then teach their specific concept to a 6th grade audience via a digital presentation. During the digital presentation, students will explain the concept step-by-step, using visual examples and problems to demonstrate each step. Additionally, students are required to show how their mathematical concept is applicable in real life.

In this project, students must assume the role of “digital educator” and think about how to best engage and communicate their lesson to their audience (the other 6th grade students). They need to be well prepared before recording their Math Cast, which necessitates the creation of a “lesson plan” that incorporates an introduction, a body, and a conclusion. Furthermore, they have to be discerning in their selection and explanation of proper math vocabulary and academic language within their presentation. And finally, the students are taught to choose only legal graphics/music and cite their sources, when needed.

Students need to evaluate the suitability of the technology tools they will utilize throughout the project. Being that this is the first year the students come to class with their own computers, I do provide a lot of guidance towards the programs. For the visual presentation portion of the project, students can choose from the following software programs: Smart Notebook, One Note, Power Point, Word, and DyKnow Panels. For the audio portion of the project, students can opt to use Smart Recorder or Cam Studio. Each program offers something a little different from the others, thus requiring students to examine their outline/plan to guide the selection of the most appropriate tool.

Two very positive aspects of this project are that it offers students the opportunity to work in an area of interest or in an area of mathematics they feel most comfortable with, and secondly the authentic nature of the tasks enables them to truly make meaning of their topic.

Here are some final MathCasts:

YouTube Preview Image


YouTube Preview Image



Discovery Lesson for Golden Ratios

As I begin to explore new ways to teach math lessons with a visual focus in mind, I have created an activity that I am going to attempt to use with my grade 6 students. In this lesson(attached here), I will present the students with a variety of pictures, starting with faces and then moving onto rectangles and finally some objects found in nature. We will explore which ones are most visually appealing, and look for mathematical relationships amongst the ‘most appealing’ objects. From this activity, I am hoping that the students will begin to realize that there is, in fact, often a relationship between the width and length of rectangular objects; this relationship is what we call “the golden ratio.”

Once the students understand the golden ratio, we will begin to look at architecture, pieces of art, ratios of body parts, and objects in nature that all are related to the golden ratio. I may even extend it further, to those students who have a good understanding of the topic, and ask them to create a piece of artwork that incorporates the golden ratio.

I would love to hear some feedback on this lesson:

  • What else could it incorporate?
  • What other avenues could I take?

I will keep you posted on how this actually turns out in my class! :)

The Power of Visual Teaching

Nowadays, there is so much talk about brain research, and rightly so, since modern technology has discovered so much more than we’ve ever known about “the brain.” I’ve spent some time looking into attending conferences about brain research, but they tend to be generally focused. But what I am really interested in is how the brain best learns math.

At the most recent EARCOS conference 2011, I attended a session on just this topic. Unfortunately the session was a quick 45 minutes, and we only touched the surface. In those 45 minutes, of course I was reminded that the various regions of the brain have different functions, but I’ve never thought about it in terms of teaching my students math. I learned that neurons fire to both the motor cortex and also to the left parietal lobe. The motor cortex is the region used for controlling fine motor skills (i.e. moving fingers – thus the reason students start counting by using their fingers). The left parietal lobe is the region used for controlling symbolic function in language and math (number symbols). And a totally different region, called Broca’s area, is the region that processes language vocabulary (i.e. numbers written as words). When we begin to think about this in academic terms, we realize that there are several parts of the brain that students must utilize in order to truly understand a math concept.

NOTE: Most of the data that was presented that day came from a book titled “How the Brain Learns Mathematics” by David A. Souza, and I have just signed up for a summer course on just this topic. I can’t wait!

Aside from the conference session, I have also read an article written by several doctors from the Harvard’s Children Hospital titled Trigger for Brain Plasticity. The article explains that neuroscientists from this hospital have “identified a protein called Otx 2 which may trigger the brain’s ability to learn. They have discovered that this protein helps a key type of cell in the cortex to mature, initiating a critical period — a window of heightened brain plasticity, when the brain can readily make new connections.” In essence, the eye is telling the brain to become plastic rather than the brain functioning on its own.

So, put all of this together and we see that both the brain and eye function together in the learning process. This all leads to the reasoning of why students learn best visually. As educators, we now need to be focusing on developing visually-literate students. “We need to develop critical thinking skills in relation to visual images, enhance verbal and written literacy skills and vocabulary to be able to talk and write about images, and encourage students to critically investigate images and to analyze and evaluate the values inherently contained in images” (taken from The Visual Literacy White Paper written by Dr. Anne Bamford).

This year, I set a goal to redesign my geometry unit so that it was taught predominantly through the use of visuals. Since geometry is a topic that is represented by so many natural objects in the real world, I figured that was a great start to creating lessons focused towards developing visual literate students. In comparison to last year, the students performed better this year on the final unit assessment. I would like to believe it’s because I made positive changes in the way I delivered the curriculum – through visual means. I have included a few snapshots of some of the lessons  throughout the unit, as well as a student’s final project (using GeoGebra – free Mathematics software).

Snapshots of visual images from lessons:









Visual Thinking and Literacy .. in Math???

I’m sitting here in Kota Kinabalu, Malaysia at the 2011 EARCOS Teacher’s Conference following an all day session on “Visual Thinking and Literacy.”  The premise of the session was that communication occurs just as much through images as text, and that data visualization and graphics enhance our understanding of complex information as they draw upon our native ability to tranlsate visual patterns and cues. This directly relates to a fabulous article I read, titled Visual Literacy and the Classroom, by Erin Riesland. She loosely defines visual literacy “as the ability to communicate and understand through visual means.”

I signed up for this session to find ways not only in teaching math more visually, but also to find ways of getting students to produce more visually in the math classroom. Erin mentions in her article that “by educating students to understand and communicate through visual modes, teachers empower their students with the necessary tools to thrive in increasingly media-varied environments.”

Throughout the day, we were shown great videos from TED talks (see link here for one of them) and YouTube that could be used as story starters in an english or history class. We also saw several student-generated videos that were created to propose a new, world movement or teach about a topic in science. Everything I saw was fascinating, but of course, I sat in the course and kept asking myself, “How can I incorporate the idea of visual thinking to promote literacy in my math class?”

I am a firm believer that most of my students probably learn best visually, one of Howard Gardner’s multiple intelligences. And throughout the year, I am constantly looking for ways to incorporate visual models in my lessons. I have included a few snapshots below, all used in my lesson on adding integers, created in a Smart Notebook:

But as I mentioned before, I really want to incorporate ways in getting the students to produce math work visually as a way to improve their understanding and literacy in math.  Working at a one-to-one laptop school, and being aware of the digital native generation that I teach, I feel I need to take this another step … taking the students to a level in which THEY are producing work visually through the use of digital media. This is the struggle for me! How do you do this in math?

As I sit here and brainstorm, I have some initial ideas. First, I obviously need to model the concepts I am teaching visually, allowing the students to understand what they are learning. I could …

a) start each unit with a visual PowerPoint that tells a story; one that middle school students can relate to and that also incorporates the main mathematical ideas that we will be learning about in the unit. For example, at the start of a decimal unit, the story could be about downloading legal versus illegal music, and the costs that go with each (including fines for getting caught downloading illegal music). A comparison could then be made and a life-lesson taught/learned.

b) use visual images to allow students to explore/discover a specific topic. For example, show several faces of people from all over the world and ask for the shape of the face that is most attractive; move to the “most appealing” sized rectangles – get students to measure the one that most people like – determine the ratio and go back to the faces to see if they are interrelated; then look at objects in nature that share the same ratio. Hopefully this would lead them to understanding the golden ratio.

Now, I need to make the transition by asking the students to produce work demonstrating/illustrating what they have learned visually more often. Here are some thoughts that I have that are inspiring me at the moment:

a) student-developed PowerPoints that use visuals to tell a story, incorporating a math concept/topic (adapted from the teacher example above)

b) students create probability games using the flash objects (i.e. spinners, flipping coins, rolling dice, pulling colored chips out of a bag) from Smart Tools (a Smartboard resource). We could then turn our classroom into a game room, where students rotate from game to game.

c) students can make their own web quest for a specific math unit (links to definitions, graphics, instructional videos, online games, etc), providing that the teacher has outlined what is expected and what needs to be included.

As an educator in the 21st century, I need to realize and capitalize on the fact that my students learn best through visual means. Erin states it best in her article Visual Literacy and the Classroom when she says, “visual literacy instruction will better prepare students for the dynamic and constantly changing online world they will inevitably be communicating through.”

World Maths Day

I tried something new this year with my students … World Maths Day!

What a success! I introduced it as something I wanted to try and wanted them to try, but didn’t have much information to provide the students. They continued to ask more and more questions, but to no avail, walked away with no answers from me … except for that the start day would be the very next day.

I distributed a username and password to each student that I received when I registered them. (I entered all of my students, via the period in the day I taught them.) We each logged in and created our avatar … this was so much fun for the kids to do. They spent hours creating an avatar that fit them personally – and I did too!

Once the contest began, I was able to determine that the student names I entered went into a large database, based on their age group. As they participated in the contest, their attempts/scores were compared with other students in their same age group all over the world. The entire contest contained 5 levels, each getting progressively harder. All levels dealt with basic computation skills (adding, subtracting, multiplying, dividing), with Level 1 only focusing on addition. By Level 5, students were asked to solve problems from all four operations. 

***As a side note, I was a bit disappointed that the contests were only “testing” the basic skills. My sixth grade students are able to do so much more, and I felt that the levels were quite below them. I wasn’t sure how they would react to this.***

Each student chose the level they wanted to compete at and the computer program then found other students of the same age, who were also logged on at the same time, from around the world to compete with. As the program was selecting students, the world map and country flags were shown representing each student in that competition. The students had 60 seconds to solve as many problems as possible. Within the small group competition (4 students total), they were then ranked. If a student completed the round in 1st place, they received a gold medal by their avatar.  Conversely, if they got 3 wrong during the 60 seconds, they were disqualified from that specific game.

The entire contest lasted 48 hours. Students could participate as much, or as little, as they wanted. For those students who spent the most amount of time on the site, one visual image they loved seeing was the Mathometer. The visual was a thermometer-like image, and the color level would rise as more problems were solved correctly. Meanwhile, the actual number of correct problems was also being counted up.

As their teacher, I was able to log on and see results. The results told me what levels the students attempted, how many games each student tried at the different levels, what their percentage of improvement was, as well as their percentage of accuracy. Here is a snapshot of what I could view: 

 As you can see, some students visited the site much more than others. What I liked seeing was that some of my lower-end students were some of the ones who spent more time competing than others … and these were also the same students who improved their percentage of accuracy the most. Some of my original worries about whether this site was going to interest the students because of the basic level of math was no longer a concern of mine. What I liked seeing was that students were intrinsically motivated to compete against others, as well as themselves (by looking at their improvements in how many correct they could solve in the 60 seconds). Kudos to them!

If asked “Would I do this again next year?” … my answer would be “YES, absolutely!” … purely as something for students to do, on their own time, to increase their mental math skills.

6th Graders – Learning to Fly

”]Remember back in the 70’s and 80’s, when we (our generation) were in middle school? Our teachers would find creative ways to develop a competitive spirit within the classroom by designing games. The games would be used to practice anything from our understanding of math to our science knowledge and even our historical facts. We would play jeopardy-style games, family feud-style games, and other games that involved communication across groups of students. Well, I have to say, as a teacher in today’s day and age, I still do all of these things … just in a different fashion. Now, most games are created and played via the computer (in fact, my students will be playing Jeopardy, via the computer, this Friday). Most teachers have access to already-created Jeopardy templates that they can use to create their own game or digital flashcards to create games.       

Well, what about math contests? These contests could occur amongst students sitting in a room, solving math problems against each other, racing against the clock, to be the first one finished with a correct answer OR they could be done using paper and pencil, and then results submitted over the World Wide Web to an organization that has organized the competition. Or, Just recently, our school was invited to participate in a grade 6, international, online math competition being hosted by Hong Kong International School (HKIS). Although this wasn’t going to be a collaborative activity, I felt this was an opportunity to participate in a virtual competition, something unique to today … however I couldn’t fathom how this would happen, so I began to ask a lot of questions.     

a)      Would we be showing the students doing their math work through a video feed?     

b)      Do the teams need to be separated or can they all be stationed in one classroom?     

c)       What materials are the students allowed to bring into the classroom on “competition day”? (i.e. calculator)     

All of these questions were discussed during a trial run, between all 8 coaches representing 6 countries, via Skype (verbal feed only). First of all, we discovered that we could all connect and communicate through a group feed – good start. Secondly, we discussed the logistics with one another and determined that we want the experience to be a good one, so it needs to be based on honesty. The students could all work in one room; they could bring digital translator tools, but no calculators; monitoring of the students would be done by the coach on site; the timing of each problem set would be done by the coaches, and finally the grading/scoring of each problem would be done by the coach as well. Wow … what a concept!     

In a two-week period of time, I was able to elicit 12 interested sixth-grade students, making three teams of four members each. I received some sample math problems from the host school and distributed them to the students, who then worked on them individually and on their own time.     

On the day of the competition, the students were extremely nervous, stopping by my room at random times throughout the day, expressing their nervousness. Most of them had never heard of Skype, therefore didn’t have a vision of how this competition would work. That alone, probably added to their nervousness, aside from the physical competition itself.     

COMPETITION TIME – A welcome speech by the host school explaining the rules/expectations of the competition, including digital photos of each team being sent through the web; students sat individually for the “Individual Event”; students moved seats so they were sitting in pairs for the “Pairs Event”; students created rows of 4 desks for the “Fibonacci Link” event. After each round, scores were entered by the coaches through the chat function on Skype. Following all events, the scores were calculated by the host school and the results conveyed – Taipei American School WON! Cheers of joy were shouted throughout the room by my students and smiles were worn by all!     

And all of this done digitally! What a concept! Where might this lead to in the face of education and international connections? Hmmm …  

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