UPDATE: Dancing Through Transformations

So the transformation dancing is almost done (Click Here for the post). Things that I have learned from the experience are listed below as well as the documents that were given to the students:

Things that went well:

• Students were more open to risk taking since it was not done on paper. 
• It was a great activity to use for students to get to know a different member of the class. 
• Students helped each other.
• It illustrated that even though these terms have been learned before, they are not concrete in their heads. 
• Having them communicate the dance with the boxes on the ground was a good introduction to coordinate points and communicating a transformation. 
• Having the three different challenge levels allowed each groups to work on the dance for the same amount of time and with the same amount of attention to detail. 

Things that were a challenge:

• Time. It took longer than I previously thought.
• Music. Giving them music to dance to caused stress. 
• Assessment. Finding the right time/place to give formative feedback.

Things to do next time:

• No music, but indicate that they will use only 10 moves. 
• Have mini due dates for each day. Make sure that the students film their translation dance in class since the communication of it can be done at home. 
• Now that I have done this once, create a rubric that the students can refer to, and can be attached to their completed Google Doc by Goobric. 
• Determine a time when formative feedback will be given. This feedback will be on their ability to apply the terminology as well as if they are able to communicate specific steps. 

Documents:

This link is to the Google Drive folder for the class. In it are the handouts, as well as example videos for them to complete. This folder was used on the first day. Click Here. 

Learning Transformations Through Dance

I am wrapping up our first unit in Grade 7 with our Data Management unit and our infographics of Who Are We. Every year this intro unit doesn't reach the level of design I want it to, but we do reach a great level of understanding in middle school organization expectations, homework management, class routines and friendships. I always need to remind myself that I purposefully do this unit first since it allows my students to focus on these other areas and not be stressed about the mathematical concepts.

Moving forward, I can now challenge them in their thinking in the classroom. My next term is a combination of geometry, algebra, number sense and measurement. To start we are going to be looking at transformations using dance as a way to introduce the vocabulary. I was inspired by a video I saw about a year ago from Math in Your Feet of a teacher doing the activity. Here is the video and below are my outline and goals.


Step 1: Dance Creation
Students are divided into pairs. Students stand an arms length away from each other and each within a 50 x 50 cm square. In this square, the two students create a short dance that includes foot, hand and body movement. They practice this until they both know the moves and can do it in synchronization.

Step 2: Vocabulary
Students are then slowly introduced to the vocabulary of origin, translation, dilation, rotation and reflection. One person in their box is told they are the origin. The other person is the translation or reflection. After an explanation of what there terms mean, the students then dance their dance in both situations. For the translation, nothing changes. Students see the movements are the same, but just not in the same box. However, when a reflection occurs, the origin does the original, while the other student completes the reflection. You can probably picture what happens with the others as well. Students practice each of these, switching who is the origin.

Step 3: Combination and Share
Students are partnered up with another group. The teacher calls out one or two terms. The students must dance their dance with these transformations. The other group is watching to see if they make a mistake and provide feedback. The teacher may say "translate, rotate 90 degrees and reflect". Students must understand what this means and preform.

Step 4: Music video analysis
As a possible homework activity, students watch a short segment of a popular music video and analyze the dance moves. They given the moves the transformation terms. They can also then identify who is the origin and also which types of moves occur more frequently. As a comparison, different people could get music videos from different countries to see what kind of transformations are more population there.

I am looking forward to trying this out. I am hoping it will take 2 periods and the homework to complete. After this, and they have the vocabulary down, we move onto geometric shapes on paper.

If you have any ideas of recommendations of how to make this better please let me know. 

Toronto Resources: My favourite sites to use in my classroom

With the upcoming Toronto election, I wanted to share the online resources that I have used with students to learn about the election, but also about Toronto as a city. So far this is my list. Please let me know if you have any others that can be added.

Great Election Sites:

• www.pollenize.org/toronto - Get to know your mayoral candidates with this clearly laid out website. The site takes information directly from each candidates platform and presents it in a visual and simplified manner. 
• FOR MATH: We have been discussing bias in data collection. We have also extended this into the election and how it can be challenging to gain an unbiased opinion of a candidate when reading an article in the paper as the author could have an opinion. This website has a disclaimer at the bottom of each page explaining how they attempt to provide unbiased and correct information. 

Great Toronto Data Sites:

• www.http://map.toronto.ca/wellbeing/ - Using Toronto Open Data, this website organizes many different indicators into various neighbourhoods of the city. Click on a neighbourhood and you get the 2011 census data.
• FOR MATH: Students are able to calculate percentages from the data. They can then compare various neighbourhoods and their populations or different indicators given. With the election in play, they can also consider what platform topics the neighbourhood could be most concerned with based on the indicators. 
• Open Data Toronto: This is a great site providing direct access to all the data that has been collected in the city. 
• FOR MATH: I have used this in my class many times from analyzing tables to creating infographics to display the data clearly. I have used the Food Bank attendance as well as Bike data. This raw data is easily accessible and related directly to Toronto students. 
• Toronto Demographics: This site is where the analyzed data from Open Data Toronto is placed. I have used this site for the Ward reports. 
• FOR MATH: I have used the reports here with students to complete a "If Ward 11 went to my school" or "If Toronto went to my school" project, which runs just like the "If the world was 100 people". The difference with this project is that students can think about the data and consider if they feel our classroom reflects Toronto. This can start great conversations about diversity, civic responsibility and who are we in our community.

Great Toronto Article Sites:

• Spacing Toronto: I am a big fan of this magazine, especially for articles for Middle School students to read. The focus of this magazine is how design is important in the creation and sustainability of a city. Articles are short and can be a good way to start a conversation about a topic or Toronto issue. 
• BlogTO: I use this site to become aware of great activities and events that are occurring in Toronto. I believe that if I want my students to be active citizens, than I must explore the city as well. The events section outlines great events each day and weekend.

Creating Equations: Starting with Rates, Ratios and Percentages

Determining how to launch a middle school math class was a challenge for me. Having students coming in from various schools and backgrounds, I had no idea what baggage, good or bad, they were bringing with them. It is a great challenge to learn about each student, their learning styles as well as background while trying to teach them something new. For the month of September, I like my students of all levels, to feel successful in our math class. This helps create a positive feeling over the subject and also helps create a sense of community where we can all learn.

For the past two years I have started with percentages, rates and ratios. For some students this is an area of confidence, but for others it challenging due to confusing word problems and mechanical calculations that can become confusing. The goal is that we move from this into creating and balancing equations. Deeply understanding equality is very important for the start of algebra and balancing equations, and I felt that we could introduce this with percentages, rates and ratios.

To do this, our class focused on equivalent fractions. To solve each of their problems from rates, ratios or percentages, students created equivalent fractions. Identifying what is the part and whole in the problems and how they are equal to another part and whole.

It took two weeks, and three classes a week for the students to really grasp the idea. However, what I found was that students were reading the questions, analyzing the values and thinking about equality more than when we learned how to solve each of the problems in the traditional "divide the numbers and multiply by 100". Those students that came into the class with these calculation methods and didn't understand why they worked, found the equivalent fractions a longer thing to do, but they understood why they were doing these calculations.

Most importantly, students are identifying that what is on one side of the equal sign is equivalent to the other. They use the term equivalent in their explanations and when they are working on a problem. I know that this will be very helpful as we move forward to making one step equations where students rebel at the idea of writing an equation and just want to solve. So far it has helped those that are struggling, and given a new challenge to those students that already feel confident with their rates, ratios and percentages.

I have attached some questions that we did as a class later on to see how we set up and solve our fractions.

Why I (half) Use Khan Academy in my MS Math Class

Over the past year I have read numerous posts about the pros and cons to using Khan Academy. After reading many of these, and now that Khan Academy has come out with new features, I wanted to put my two cents into the mix as to why I feel that I "half" use Khan Academy.

Teaching Student Individuality
I introduce Khan to my students on the first week of school. Students create accounts and add me as their coach. As we do this, we also have a conversation about who we are as learners. We talk about how important it is to understand how each person learns differently and needs different supports. We also discuss how a mature student is one that celebrates their own learning needs and finds their own right path to success.

I ask students to think of a time where they felt that they were learning differently than the other students in their class. A time where they felt they needed something different. Everyone can think of a situation that this happened, either that they were ready to move on, or that they just needed more time. This is when I introduce the Khan quizzes. We talk about how each student is able to practice a concept as many times as they need, without waiting for a teacher to tell them to, or that they can move ahead and challenge themselves with a new idea. They can then work on something as many times as they need to, at any point in time without any consequences. We then share and celebrate times where students felt different than others in their learning. Putting these feelings in the open in a middle school classroom can create a classroom culture of understanding and support.

Creating Student Directed Review

When I started using Khan, I would assign quizzes as homework, but I realized that this was not following the culture of student directed learning I was trying to create in my class. The minute that I stopped assigning quizzes, students saw them as a place to make mistakes without injury. A place to practice and test their ideas with immediate feedback. Prior to assessments, they select their own review questions based on their own needs and create their own study plan. With the immediate feedback from the quizzes, they can gauge their own needs and made adjustments as needed. By the end, they have a great sense of empowerment and ownership of their learning. They were the ones that made the plan, did the action, and then came out with the final result. I feel that for a middle school student, this is a very important lesson.

Providing Vocabulary to What They Learn
I have also used Khan as a way for students to identify what they have learned. At the start of a unit, I give the students a list of concepts that we will be learning. We call them the "building blocks" as they are the more calculation/knowledge based concepts needed for their curriculum. As we explore the concepts in class, students are told that we are looking at concept #6, or applying concept #4. Students can then refer to their concept chart to see what these could be called. Along with this chart, I attach links to Khan quizzes. I do this because I want the students to be able to look back at examples of things that we have done in the past, and see how they build on top of each other. They can also then practice a specific skill if necessary.

This year I saw a new benefit to linking the Khan quizzes to each concept. My students now can tell me that they are having challenges with the distributive property because they don't fully understand negative numbers. By seeing how the concepts build on each other, and not as separate entities, they can find the specific issue for themselves. They can go to a Khan quiz and see concepts as many times as they need, making them more familiar with the smaller building blocks. Compared to my past experiences I would have students say that they can't do any math and would put up a wall for moving forward. Now, I have students saying that they can move forward as long as they go back and practice an earlier concept. This was an amazing thing to hear from a student, and something that we celebrate together. If a student can identify a specific challenge rather than feeling it is EVERYTHING, they can feel there is a way out of the maze. The best part is that they become their own guide rather than depending only on the teacher. I have really enjoyed this aspect!

How I Don't Use Khan

I do not use the "flipped" approach that Khan was originally founded on. I do make my own videos, that I post after we have explored a concept in class, but I feel there is a part of learning that is missed if a student doesn't have a chance to explore an idea before they are walked through it. I feel that a student should have the time and opportunity to think through a new concept. To be able to ask themselves:

What looks familiar? 

What looks new? 

If I could change one thing about this problem so it looks familiar what would it be?  

What do I think my first step is going to be?

 I feel that by giving the students a chance to explore the ideas, they start to develop their own problem solving skills.  The end goal is to develop their own routine to find a starting point for any question that they are presented with. I feel that if a student is walked through the steps they don't have this opportunity.

Final Thoughts

I am very thankful for programs like Khan Academy. They allow my students to feel that they are more in control. They determine what they need to practice and when. They also start to celebrate their own challenges and their own solutions. I also appreciate how they are free, and my students can continue to use it long after they leave my class.

I feel that Khan can be a great tool if used in the right manner. For me, that means there is nothing assigned, marked or expected from students when using this program. The less I tell them to use it, the more they do. My next step is to figure out how my students can start making their own Khan academies online, to share and collaborate with each other in a program that gives immediate feedback like Khan. I guess that is the project I could assign my students exploring coding as an extension project. See what their first step will be to this new challenge.

Flipped Mastery: Finding a Balance for Middle School Students

For my upcoming unit of Patterning and Algebra, I have decided to run the class on a Mastery Method. I have spent the past two weeks setting up the program, marking plan, support materials and just released it to the students this week. I was surprised to then see two articles posted this weekend, one from the New York Times and the other from David Wees which both made me reflect upon my methods and goals.

The New York Times article In 'Flipped' Classrooms, a Method for Mastery, Tina Rosenberg summarized the challenge of a traditional class room as "the teacher must aim the lecture at the middle, leaving the faster learners bored and the slower ones lost". I have enjoyed using a Challenge by Choice approach to differentiate my teaching for my students. They select the level of challenge and support that they would like when learning a new concept. The issue I was having with using this method was that I was dictating which concepts we were learning and when. Students still enjoyed selecting their level of challenge as they could move slower or faster depending on their personal needs at that time with that concept.

However, looking forward to our algebra unit, I know that my students are coming from a wide range of backgrounds, and some have already covered this material. Due to this I wanted to provide the Challenge by Choice teaching style, but also with the student selecting which concept they wanted to explore and when. My solution to doing this was to combine the Challenge by Choice with a Mastery Method of teaching.

To make this happen, I have broken down the unit concepts into small, understandable steps for my students, each with their personal copy. I took this idea from Dan Meyer after reading his post about his checklists for students to track their learning. Students are made aware of which concepts we will be exploring in the upcoming week via an email and announcement on Friday. If students want to, they can go to another document that outlines videos that I have made or found as well as practice questions about this topic. They can explore the concepts ahead of time, practice, and then come to class knowing what kind of support they would like to have (Green, Blue or Black). When I introduce the concept, students can then decide if they would like to explore the concept together, or if they would like to move ahead and explore an additional concept through online resources, in class activities or with peers. As stated in the Times article, putting this together has been almost having another job, but I know that by having the resources available will allow the students to move at their own pace.

The plan for tracking the students progress is through the use of Mastery Quizzes. Students will sign up each week and identify which mastery quiz they would like to complete. These are formative and they can take them as many times as they like. To be a master, they need to get 4/4 on the concept twice. Students track their progress on their concept check list sheet and I do the same in my notes. It is through these quizzes that students can show me that they already have understood a concept and so they do not need to be in the Green group with me, but can move ahead. If a student has not preformed a mastery quiz on that concept, they are indicating that they would like some support walking through the concept.

In the end, all the students will still write a signature assessment (test) displaying their understanding of the unit. The difference is that they can select how they progress from the start of the unit until the end, not having to move at the same pace.

David Wees made some valid points in his post that made me reflect on my plan to use online resources like Khan for students to practice.  David identified the following challenges of only using online assessments or learning tools when looking at its use at his son's school:

• It did not measure his ability to explain his reasoning to others.
• It did not ask him to show multiple solutions for finding his answer.
• It did not present a meaningful context, and measure my son's ability to apply his understanding to that context.
• It did not check to see if my son had gained any transferable understanding.
• It did not allow my son to talk to peers about his solution.

I am going to keep David's comments in my head as I move forward. My goal is to ensure that those students that are moving ahead are also needing to think collaboratively and be challenged when in the Black or Blue groups. I will remember to think that online tools should be used as a way for them to track their own learning, but not as the way for them to display it. 

If you have any experience with a Mastery based program, I would love to hear or read about your experience and appreciate any advice you can give. 

My Grade Book: Tracking Progress, Not Product

This year I am trying out a new way to set up my grade book. My goal is to better see the progress my students are having in the class, identify areas where they are being challenged and provide extensions when they are showing mastery.

My grade book last year looked something like this:

	Formative Fractions: Quiz Sept 15 (/12)	Formative Percentages: Quiz Sept 30 (/15)	Summative: Test Oct 6 (/35)
Student X	7 = 58% Knowledge: 2/3 Thinking: 1/3 Application: 2/3 Communication: 2/3	12 = 80% Knowledge: 3/5 Thinking: 3/3 Application: 4/5 Communication: 2/2	29 = 82.5% Knowledge: 13/15 Thinking: 6/7 Application: 5/8 Communication: 5/5

In Ontario, each of our assessments are broken into four learning categories; Knowledge, Thinking, Application and Communication (Achievement Charts). Even though with this method, I am able to see that my students greatest area of challenge is in the application area but I can not be specific with my feedback about what concepts, or steps they should take to improve. I can only be general or have to sit down and go through the assessment with them to identify how they could improve. I found that a week later, I would only know that I would need to help this student with their application questions, but I would have no background as to specific concepts, or past areas of concern to adjust my teaching methods. 

To help give a better picture of each student and their progress and growth, I looked to Standards Based Grading for support. My school does not grade using this method, but I thought that if I used it in my personal grade book, it would help provide more meaning to my grades and therefore impact my teaching. My school grade book still looks like the one above, but now my grade book for each unit will look like the following:

Diagnostic		9abcd	4b,7a,b	8a	8b	7b	5	3, 4a
1st Assess	Formative		1ab	1c	1d	1b		2
2nd assess
3rd assess
First Name	Last Name	Algebra Awareness	Add and subtract fractions	Multiply fractions	Divide fractions	Convert improper to mixed fractions	Create equivalent fractions	Order rational number
Student	A	NC	VG VG	NI VG - formative	NC VG - formative	VG VG	G - mixed challenge	G - issue in boxes VG - formative
Student	B	Guess and check	VG VG	VG VG	VG VG	VG VG	VG	VG VG

This was the first few columns and refer specifically to specific concepts. As you move further along in the grade book, it then shows results for applications of rational numbers from word problems etc. 

With a lot more lines, it looked more confusing and more work, but I feel it provides a deeper picture into each of my students. I have put more emphasis on the concepts, taken directly from the curriculum, and now break up my assessments into these rather than the other way around. I have also indicated what question on each assessment referred to each concept. This way I can also ensure that each concept will be assessed multiple times and that students have been given feedback. Now a story can now be told about each learner:

Student A:

• From her diagnostic, Student A showed that she was comfortable with adding and subtracting fractions even when there was an improper fraction involved. However, she showed that she needed improvement in multiplying and dividing fractions as well as the rational number on a number line. Specific support was provided for these areas, and with the second assessment she has shown improvements. The student can be congratulated specifically on her improvement in each area.

Student B:

• From the diagnostic it was aware that this student already had the skills in these areas. Throughout the following class activities, she was encouraged to challenge herself with Blue or Black level activities. In her following assessment she continued to show a very good understanding of the concept and she will be encouraged to explore these ideas further with individualized questions. 

For me, it helped to see if students were continuing to struggle on a specific concept and more direct instruction or support was necessary. Also, I am able to say to Student A:

 "I saw that you have made a great improvement in your dividing fractions. Thats great! What did you do to make those improvements?". 

By identifying their specific achievements, I hope that we can celebrate together, but also reflect on their process. How did they improve in this area? What strategies did they use? What resources? When a student sees that they are the ones that made that improvement, I am hoping I can refer back to it when they may come across a challenge in the future. Also it allows me to celebrate each student because each one will hopefully show a progress on one concept even if their overall result is not displaying this. 

If you have a way to break down your grade book into specific concepts that is working for you, please let me know. I am hoping to make changes throughout the year to something that communicates the learning process.