Online Tools: Math Manipulatives

Having math manipulatives in class is always helpful to show our thinking in different ways and we usually encourage students to use them, but they are more important for use in my role as "teacher". I like to think that I can communicate ideas clearly with my voice, but I know that I am only saying the words that make sense to me. If I show a picture I can allow my students to use their words to share what they see.

The following are free online math manipulatives that you can use with your students. I have seen them be used when doing a PD session by Dr. Theresa Wills. During her classes, she provides the links to the sites that best match the problem she is presenting, encouraging students to go and use them to communicate their thinking. She usually presents 4 tools and encourages students to show their thinking using more than one. Students can screen capture or copy what they have created into a group slide/document, showing their thinking and helping them communicate with their peers.

Math Manipulatives:

Unifix Blocks: A simple drag and drop tool that allows students to create stretches of blocks. They can represent anything from patterns to measurement to ratios.

Cuisenaire Rods: Quickly drag the control to create bars of different sizes. Click and drag them onto the mat. They can be used to represent anything you need.

Ten Frame: The Ten Frame was a new manipulative for me as a MS/HS teachers, but I feel it is important to be aware of all the tools students may have used in the past that they connect with. I can see how this can also be used to help with integers. All students need to do is drag and drop.

Number Line: I use a number line in my class all the time when exploring ratios, rates, integers or just general problem-solving. The tool requires just a few students to start playing with it to see what it can create. Also, the information button provides a clear explanation of all the tools. Have students create their number lines, take a screenshot, and share them with the class.

Algebra Tiles, Base 10 Blocks, Number Lines and More: This site provides lots of visuals tools. By having the blocks and number lines in one location, students can easily combine the tools together to represent what they are wanting to create. There are also backgrounds that can be used that can support algebraic reasoning.

GeoBoard: Just like in person, but now without the hassle of trying to find elastic bands or having the plastic nobs break off. Students can use this to explore various geometric representations.

Fraction Bars: Create your own fractions in either a rectangle or a circle. You decide how many parts it is out of and then add the colours as you need. This is a great tool for students to quickly create the fraction bars they are wanting to represent, make them the same size and compare values.

Pattern Blocks: Never lose the blocks again. Students can pull as many as they need to their board, manipulate the direction and copy/paste to create patterns. There is a protractor that snaps into place to measure any angles. This can use used for patterns, geometry and number sense. There are also backgrounds that have shadows of shapes, allowing students to cover them with the tiles.

Additional Resources:

• Math Learning Centre: Many of the tools listed above are on the site. There are others as well as additional resources to explore
• DiDax Virtual Manipulatives: Some cross over with those in the Math Learning Centre, but there are a few new ones: 120 board, balance boards, spinners and more.
• Math Playground: Many of these require Flash to work which may cause problems with access by students. However, there are lots of options here as well.
• Geogebra Graphing and Calculator: This site provides a geoboard, calculator and graphing software. Students can save their work for later review.
• Desmos Graphing: Students can quickly create a graph, build a table of values or write a function. When finished, they can screenshot the image and add it to their work.
• Desmos Scientific Calculator: Use this as the class scientific calculator, making it easy for everyone to have access and talk about how to use the same device.

Digital Tools: Opening my eyes to online learning

I am now entering week 10 of online learning, and it has been a pivot. I decided to lean into the pivot and use these weeks as an opportunity to explore. In my explorations, I came across Dr. Theresa Wills. She is a professor from George Mason University and has been teaching math online for years. I forget how I found her, but she has opened my eyes to what is possible. Since she has been teaching online for years, her strategies are very well developed and the free daily PD she offers allows anyone to learn from her. I sat and watched many of her recordings and learned the following:

• Teaching is a skill you develop over time and with practice. Teaching online means applying the skills I have developed but in a new medium. I have to now practice these tools, giving myself the time and play to learn them. I can't expect to be good at this unless I practice. 
• There are so many other people who have been doing this for a while and doing it well. There are benefits to this method of learning that I can learn and help my students, now and in the future, if we go back to class. 
• The online teaching community is supportive and caring. I have taken two of Dr. Wills PD sessions and all the teachers I have been grouped with make me feel supported and help me where I am at. 

I recommend that anyone who is teaching online to explore what Dr. Theresa Wills is doing to develop community and collaborative learning in her classes by using Google Slides.

This is the video that hooked me. I hope that it hooks you. 

Goals: 2017-18 School Year

At the half way point through the summer, I found the #MTBoS Sunday Funday prompt of "Goals" to be a nice way to have me start the slow transition back to school mode and back into blogging. Even though I am aware of the benefits of writing my blog, this past year was not a good reflection of that... which leads me to my first goal (and what I hope #MTBoS will help me keep up with).

1. STOP and Reflect in the present: Use my blog as my tool

Reflection is a process that I always have my students do throughout a day/project/unit/hour, but I find that I am not modeling what I feel is an important strategy. Yes, I reflect on my day. Mainly on my bike ride home considering what I will do the next. Or even at the end of a project, considering what I liked, what I would need to change or even complete a tuning protocol. But all of these reflections are after the event has happened, never in the present. I am hoping to use this blog as a means to get a greater sense of the regular pulse of my practice and consider the pulse of my students' overall weeks.

2. Explore Personalization in Greater Depth

I like to think that I provide opportunities for personalization for my students. This happens in their ability to self-select challenge levels, methods of instruction during class time and also to use projects as a means to make the end product their own. What I am still grappling with is the personalization of content. I complete diagnostics at the start of all units, identifying where students are in their understanding/mastery of concepts, but I do not feel that I am using this information fully. I am always challenged in my mind about what going into greater "depth" of a concept looks like, rather than jumping forward to a new one once a student has shown understanding.

3. Getting students to ask Math "I Wonder" questions like we do in Science

I teach Math and Science for Grade 7. In Science, once I have seen students demonstrate the learning goals of the unit, they naturally build on them and ask amazing "I Wonder" questions which drive them to explore further, make greater connections to the content explored and the world around them. I want to find a way to make this routine present in my Math classes as well. I find that my students (and I) do not ask the I Wonder questions, but wait to be presented with a problem to solve. I am hoping that exploring Personalization will help support this, but I also know it is a mindset that I need to change in myself first. As a lover of math, I have never asked my own "I wonder" questions but instead waited for fun problems to solve. 

Patent Laws, Areas of Shapes and Launching into Structures - June is on its way!

It is weird to think that May is already here and June is just around the corner. However, when I feel the energy in my classroom, it is evident that these Grade 7 students are ready to move and get going into action. This week the goal was to have a short launch into their activity and then send them loose to explore, try and play. The learning goals for this week were:

• Through understanding forces, we can prevent failure of a structure
• Understand area is the space taken up by a 2D object
• Explore the relationship between finding the area of a rectangle to the creation of a formula for the area of a triangle

Science:

This week was the wrap up of the solar oven project since we cooked our s'mores on Friday. With the twist of having students decide if they should make their results of experiments for public or private use, I wanted to take time to explore how this is applied in the world outside our classroom through patents. I decided to have a discussion period where students would understand and question how patents can motivate as well as make it difficult to innovate. 

To launch, I used the Poll Everywhere app to have the students share anonymously how they felt about making the results of their solar oven experiments for others to use. Through the different questions it was identified that:

• In this project, students made all of the experiments public for others to us, but if there was the option of charging their peers a chocolate bar to use their ideas they would have done so. 
• If they knew that not everyone in the class had a chocolate bar to spend, there was a slight shift to making it public but the majority still remained keeping it private and charging. 
• When asked what they think causes people to want to create inventions, the highest ranked choice was because they had a problem to solve, but also the idea of financial rewards appeared. 

After discussing the results of our class data, I walked them through the process of getting a patent and outlining the time and investment of money that is required. We searched on the international database of patents to see if an idea we had for our solar oven was already created. They found this challenging and time consuming. They also saw how inventions that are patented show how to make and produce the invention to everyone online, which they saw as a way to spark ideas in others...if others could find the patent. 

We then took time to ask why inventions had not been created to solve problems such as clean water, when we have made great improvements in cell phone technology. By talking through different world views, they were able to identify that the financial investment required to develop a product would then be gained back by selling the invention. However, if the people needing it have no money to pay, than the inventor would be at a loss of money.

I was really happy that we had this conversation as it allowed the students to see why some of the world's problems have not been solved due to issues that they have never made connections with before. The conversation was enjoyable and worth the period that we spent on it for sure and I would do it again. 

Here is the slide show that was used: https://drive.google.com/open?id=1QVrhWcdUsVrspBD0OUMe9Q_1XdaqrlEZBpfen01sp6o 

To get ready for their upcoming structures unit, they are doing a homework assignment that will let them build and also collapse different structures. It is called Catastrophe and the developers have done a wonderful job of applying the laws of physics to the designs. My students have already started using the terms tension and compression without having learned it in class. 

The assignment they are working on is: https://drive.google.com/open?id=1N3Q3ELicDaoT5lAhIY5IwIIWHlU4slCXvFPrDrjK3m4

Next week is the launch of the structures unit and they will be working with another class. Lots of hands on building and exploration to do as we go into the end of the year!

Math: Finding Area

I was able to participate in a Lesson Study done by the Junior School teachers this week which focused on the development of understanding of area. With a focus on conservation and additivity when finding the area of irregular shapes. During the conversation, the idea that students forget these concepts as they begin to learn the formulas of shapes. With this in mind, I wanted to teach the area of a triangle by starting back at the start of understanding area. 

To do this, I told the students that they would be erasing their brains of all past knowledge and we would be progressing together. We talked about how measurements were originally taken by using body parts, but that different sized people would have different sized hands/feet. Then standardized units of measure were created so that everyone knew what was being talked about. We then explored why they were called units squared. For some students they had not thought of this since their younger years, and only now were able to grasp the concept. It was a short review, but important to understand that it is the total number of square units. 

We when looked at the area of a rectangle and saw how it is an array. You have for example, 10 groups of 6 boxes in the rectangle, so we can use that to do it faster. Students they made the connection that this would relate to the base x height formula they had learned. 

Finally we did a paper cutting exploration to show how two triangles make one rectangle. They understood that if we know how to find the area of a rectangle, than cutting up a triangle so that it fits into a rectangle allows us to use our array understanding to find the area. This was then connected with the formula that we then developed together. 

Once all students felt confident with this task, they were put into groups with their own shape that they needed to create a similar slide show showing how to change the shape back into a rectangle and then use this to develop a formula. Groups were arranged on purpose by processing speed so that they could think through the problem together and no one would be left behind. This was because the goal of the lesson was for them to think deeply about how conservation of area can occur. 

Now, they are creating their slide shows and will present to others in small groups next Wednesday. They will have the slides shared as their own "notes" to refer back on for their homework. This will be a good launch for their individual solving of irregular shapes as well. 

Slide show used: https://drive.google.com/open?id=1AZP9F2b9kqAH7oDlLUaTZ7ARx8j5nGHvK8Xe8yv45L8 

Solar Ovens Week 2, Oral Evaluations and Climate Graph Intro

So, perhaps as predicted the solar oven project too a little longer than predicted. Due to bad weather, we didn't get the best days of testing. This resulted in the exit interviews starting on Thursday rather than Wednesday and will probably enter into next week. However, we are ending today with the big test of the ovens as well as using them to make SMORES! This last part is the surprise to the students.

Here was the week:

Solar Ovens:
Overall a big success. Students continued to think creatively about how to make adaptations to their ovens, but also find the supportive data in their peers experiments. It was interesting how every solar oven experiment was made public for other individuals to use. This was a big change from the start of the project where students were wanting to keep ideas and results private. Next week we are going to be exploring how this decision to apply patents/copyright on research results can be challenging for overall innovation, as well as encourage it.

The new thing this week are the exit interview. Students are completing a verbal evaluation where they need to identify the modification they made, explain how it harnesses the sun's energy and provide evidence from their peers to show that it works. Providing a verbal evaluation has been great for two reasons:

1. Students who are verbally strong now have the chance to share their understanding in a manner that suits their preferred communication style. They come prepared, but can explain further without being concerned about the time it takes to write down their ideas. 
2. Feedback and clarification is automatic. I get very frustrated with written evaluations where the student didn't interpret the question correctly and therefore did not put the right answer down, even though you know they know it. By having it done verbally, I can pose the same question, but then ask clarifying questions afterwards to see if they do understand the material. It is also a great chance, once the evaluation is completed, to provide feedback on both their ability to do a verbal evaluation, but also address the misconceptions or misunderstandings they have about the concept rather than wait 2 weeks to get back their written work. 

Students are coming well prepared which is a big help to me. So far, the results have been quite good as students in this model are better able to share their understanding. If a student is not prepared, they have not been meeting the expectations and have been asked if they would like a chance to re-do or stay with the result. This has also been interesting. 

Materials for this week:

1. Rubric for the exit interviews
2. Homework on renewable resources

Climate Change and Climate Graphs:

The presentations of each of the IPCC's climate graphs were completed this week. Now a bulletin board has been made outside the classroom to show the connections between different graphs and how the data can tell a new story. This has been effective for the students to see the larger picture of climate change, with the supportive data. 

They also took time this week to explore climate graphs (showing temperature and precipitation). This has been very helpful for the Social Studies teacher who used to take a lot of time to explain how to read them. By having it as a part of their homework and an in class activity, the students are learning how to read them with me, but then going to apply the information in their other class. 

Materials for this week:

1. IPCC climate graphs
2. Making connections activity
3. Reading Climate Graphs homework
4. Reading Climate Graphs Homework Check In

Climate Change, Solar Ovens and Exploring Patent Law

Coming to the end of the year, there is always the challenge of how to spark Grade 7 students to keep going as well as create assignments where they can also explore their developing independence. The class had four learning goals this week:

• Science: Identify how heat is transferred and how heat loss can be reduced. 
• Science: Look at trends and evaluate the amount of greenhouse gases accumulated over time and propose courses of action to reduce the amount of greenhouse gases in the atmosphere. 
• Math: Make inferences and convincing arguments using data and the analysis of data from charts, tables and graphs that compare two attributes investigated. 
• Math: identify trends/patterns present to come to a conclusion on an argument

Science: Solar Oven Development

This week was day 2, 3 and 4 for the solar oven project. At this point, students had already determined if they wanted to be in a group, or working alone. Many had already identified the modifications they wanted to make to the "base model" and created experiment planners to test their new ideas. They had also thoroughly read through their peer's lab reports from the individually created heat labs completed over the March Break to find ideas and evidence for possible modifications. 

I really appreciated how the students bought into the hypothetical situation of being in an information bubble. They have only the results from their March Break lab reports to reference as evidence for a design modification. By doing this, students were reading through each others labs with a fine tooth comb. What was the biggest take away was how the students were trying to find ways to use the experimental results of an experiment involving putting an ice cube in a cotton or wool sock to justify a modification to their solar oven. They were able to take the results and apply them to a new situation effectively. However, hearing their discussions over how the data could show their modification showed their deep understanding and also some misperceptions of heat transfer that I had not heard until this point. 

Students who had decided to complete their own experiment are now collecting the results and determining if they want to make the results public for others to use. It was also interesting to see their excited faces during the first trial and seeing the results coming in for each modification. Students were then asked by their peers if they would make the results public or not. It was great to see students challenged with the decision of if their ideas should benefit others or just themselves. We will be wrapping up this conversation next week with an analysis of various situations where the decision of sharing scientific results for others use occurred and the outcomes afterwards. Having Grade 7s debate the purpose of copyright and patent laws will be very interesting now that they have their own personal experience. 

Documents used this week:

1. Solar Oven Student Handout
2. Solar Oven Design Template
3. Solar Oven Experiment Planner
4. Solar Oven Exit Interview Rubric

Math: Reading Graphs With a Focus on Climate Change

Since creating their lab reports from the March Break heat labs, they have developed an understanding of what is required in a proper graph. What we have been focusing on is that each graph has a story to tell, and that this story was was only told because someone had a question. When reading graphs their job is to identify what the question was that was asked and how the graph tells the story of the answer. 

I also wanted students to realize that reading a graph is not difficult, but requires them to slowly decode the information. Even the most confusing graphs can be broken down into parts that they can work to understand independently of each other prior to bringing the ideas together. 

There is a range of abilities in the class for how students can interpret visual data. With the range, some students are still working on reading a line graph while others are ready for a greater challenge. To ensure that all students were being challenged in this area, I wanted to find graphs that were all trying to tell the same story, but in a different way. This way my students, no matter which graph they received to work on, needed to tells its story to the rest of the class so that the big picture of climate change could be understood. 

To do this I went to the IPCC and used their graphs and data that explain climate change. I broke students up to work on a graph that reflected their need for challenge. Upon receiving their graph, they had 10 minutes to work independently to work through the decoding document. Then, after the 10 minutes they joined up with the rest of their group to share what they had decoded as well as where they were stuck. The final goal of the week was to create a slide show presentation to share with the rest of the class. In this presentation they needed to show the graph, explain the graph by decoding it, identify the question that was asked to make the graph, the answer to that question as well as the "why should we care". We have now started the presentations and it is really interesting to see students make connections between the stories their graphs told to the stories being told by other groups graphs.

The next step is that a board is going to be made with all of the graphs. Students will then use string to make a physical link between two graphs (one being their own) and identify what story the two graphs together are able to tell. They will then need to explore what next steps can be made to improve the outcome

Documents used this week:

1. Tuesday Slide Show Presentation
2. IPCC graphs for each group
3. Graph decoding document

Making Math More Like Science

This is my second time teaching Grade 7 Science, and once again I am blown away with the simplicity of the material but how it "blows our brains" as my students explain. As a class we have spent days talking about The Particle Theory. These 5 postulates have caused us to question everything from why does it take longer to make a cold tea than hot to the fact that we are made of the same stuff of dinosaurs. What would seem like 5 simple rules has caused all students in the class to question, explore and expand their thinking.

Having taught math for the majority of my career, I am used to parents and students feeling that the same enrichment and challenge only comes from the exploration of material beyond the curriculum. We have to leave the material of Grade 7 so that a student can become equally engrossed and inquisitive about the material as their peers. However, from observing my Science students I challenge this full heartedly. As we explore the same concepts of Science, each student is driving their thinking forward from their own questions. No new material is being presented to them, but they are using their current knowledge to ask questions and see how they can apply this thinking to the world around them. The difference I see from this and a math class is that math does not encourage student driven questions. There is a sense that an order must occur in the learning of material and that the teacher should guide it. I want to put this thinking in the garbage this year and make it so that math and science are structured in the same manner; the presentation of foundational concepts and the time for students to explore and make connections on their own.

This will be a challenge. I know from personal experience that students are taught to ask questions in science since these exhibit wonder and excitement about the material. Asking questions in math class could have a very different reaction from peers and the teacher. It could indicate an inability to grasp the concept, not able to focus on the prescribed task or "not what we are thinking of at the moment". Students, and parents, are trained to learn, practice and then perform rather than the science of learn, question, explore and perform.

To do this I have made my students first math project to be one where they need to ask their own question where proportional reasoning is the base. How far they push and go with the ideas is up to them. My last blog post goes into more details of the project. However, over this past week I am more convinced that a great exploration and student driven activities are necessary in math classes to develop the math students my high school coworkers are hoping to have come their way. They are wanting to have the thinkers, and not just the calculators.

Who is Doing All the Work?

I made a new motto for this school year: Get the Students To Do the Work.

It came from a volunteer training program for a call centre I did over the summer, where my greatest challenge was to remember to let the caller do all of the work. My job as the volunteer was to hear their ideas and then reflect them back. It was hard for me to not go straight to thinking of solutions and next steps. However, I found that being able to provide an open space for the caller to explore an idea they had, gave them more clarity in the end rather than me trying to pipe in. So this is what I am exploring this year. Giving the students the opportunity to start the exploration, rather than the strong teacher guided exploration.

I also ended last year with the goal of making my classroom and products created be more “grade 7”. I have always had the tendency to create projects or activities which are great, but take the time and attention of a Grade 9 student. I would do this because my students were capable of doing it with the right support, but they lost the time to think of their own ideas and questions. The final product looked amazing, but it wasn’t with a clear student mark on it.

So to reach both of these goals I have started the year with being open about what the learning goal and standard they are going to be evaluated on, and then asking them to create their own project to demonstrate this. Our first learning goal is the understanding and application of proportional reasoning and to demonstrate this using a variety of tools.

Click Here for the Project Outline

So to start, I told the students we were going to do a project about proportional reasoning. The next step was for them, at their desks to research what proportional reasoning actually is. We did a placemat activity at their tables and then came together as a class to share what we had found and created a definition of proportional reasoning. 

This activity was a great equalizer for the groups. Students of all math abilities had equal opportunities to provide input with their research. Also, since they all have had exposure to this concept since their early primary years, they all could relate to what was being found. We came together as a class to share our ideas where I acted as a scribe on the board, almost in a Bansho manner. They then went back, added to their sheets. Many were not fully completed, but my plan is to present the placemats back to the groups midway and at the end of their projects for them to add more detail as they understand and explore.

Their next step is to create a question that they find interesting and want to explore that uses proportional reasoning. The week before the class had worked to find out the cost of my grilled cheese sandwich by creating a question ladder, asking questions and using proportional reasoning skills. This was a diagnostic on my end to see what natural instincts to solve this kind of question would be used by each student. We created more questions together, some similar to their grilled cheese sandwich, and others more abstract. They are now creating their own question and developing a question ladder of their plan to solve it. By the end of the week students were thinking of questions that they were interested in, and therefore ones that they will persevere through determining how to solve.

Next week we are going to be looking at different types of questions involving proportional reasoning and thinking of the various strategies that we can use to solve them. All of these strategies will come from the students as I sit back and observe. Fingers crossed that is!

End of Year Reflections

With my first year teaching Grade 7 Math and Science over, I have come away really loving this year. Compared with my past few years where I have taught four or five classes, working with only two classes over two subjects and homeroom made the year feel quite different. I felt that I worked more closely with the students, parents and supports in the school due to having half of the number of faces and stories to work with. Yes, the downside is that I didn't get a chance to meet the whole grade, but I am looking forward to being in the same class and having the same set up next year. With this in mind, I have made my "Affirm, Refine and Aspire" for next year. 

Affirm:

The big thing that was affirmed for me this year is that I do love Middle School. I really enjoy how my students are wanting independence in their learning, want to explore the world around them, play games and challenge themselves, me and their peers. I also love how forgiving this age group is if you are honest with them. I have learned that once they feel you are on the same "team" as them, they will be alright with me saying "hey, I want to try something out today. I think that it will be fun, and I look forward to your feedback afterwards". They are concerned about their performance, but are open to seeing and focusing on their personal growth and goal setting rather than a percentage grade at the end. 

Refine:

This year I focused on assessment and evaluation; its purpose, goals and outcomes in my class. I started, with the support of my teaching team, using a Standards Based Grading (SBG) platform with my class. This method meshed perfectly with my Challenge by Choice activities as well as my strong belief in creating opportunities at any point for students to demonstrate their understanding. Going into next year, I want to refine how I will be using SBG. I will start the year with using Fresh Grade, a program to organize the evaluations and assessments as well as the standards. I am considering giving students the list of goals at the start of each unit and encouraging them to track their own growth over the year and take ownership over their learning. From using a quiz goal list in Khan Academy I have seen how my students used it to take the responsibility in their learning and review. I am hoping that the same thing will be possible in their "Learning Goals" (Standards) 

Aspire:

My mind, as it always has, always goes BIG with my ideas and goals. However, what has happened is that my big thinking and great ideas are great, but they also don't provide the time and breathing room for my students big ideas and personal exploration. I am setting the goal for next year to be more "Grade 7". To me this means that I am not trying to get my students to create final products that are reflective of a Grade 10, but ones that are reflective of each person at Grade 7. To do this, I am planning on taking the first three months of the school year to show my students the thinking routines, goal setting and essential skills (such as research, communication, and group work) that they will need for the year. After this, I am hoping to create more open ended projects, questions and ideas that my students will use tools described before to explore and communicate their learning. I also want to aspire to more individual check in time with students, going over their goals and what they are doing to meet the goals over time. 

To help with my goals, I am taking time over the summer to learning. I am taking the online course called "Science and Cooking" to get Grade 7 ideas for creating experiments that my students will do at home and explain the science to their families. I will explore Standard Based Grading further by reading Rick Wormeli and I am also looking at online tools that would be the best for my students to track their learning.

I also am setting the goal of taking more time for my own reflection over the year, and trying to do a better job on my blog. I want to track my thinking and development going forward so I can be better at explaining how I got to the end to others when they ask.

Hope that you all have a great summer! 

 

Transitioning to Standards Based Grading: The Evaluation

I am currently on a journey with my teaching partner to transition our Grade 7 Math and Science classroom into a Standards Based Grading (SBG) classroom. We are the only ones in our Middle School program doing it, so I have been very grateful for the ideas and feedback from others through the #SBLchat on twitter, online conferences and other teachers blogs.

This post is my reflection prior to handing back the first standards based written evaluation (test) to our students and their parents. So far, I am feeling pretty good. 

Due to the recommendations of others, at the start of the unit we handed the students out the list of the three standards that we were exploring as well as the success criteria for each. Since I am in Ontario, our success criteria was identified to be one clearly stated expectation for each of the categories (Knowledge, Application, Thinking and Communication). This way we ensured that each standard had a balance between the categories. 

Click here for this document. 

Students, with the standards in hand, didn't really get too excited. I however told them how excited I was... and they gave me a round of applause for my enthusiasm. Needless to say, that by presenting them with the standards at the start made no difference than in the past unit. So we continued on, completing activities in class, formative quizzes, challenge by choice stations and weekly homework. Each weekly quiz had a standard at the top so the students could gauge their development and understanding. The one difference that did occur was when the written evaluation time was decided, the students were not asking "Miss, what is on the test?". They all were aware of the standards as it was identified in each assignment, activity and homework problem that they did. 

Prior to the evaluation the students did a reflection identifying how they felt about their understanding for each standard (Working on, Proficient and Mastered) and they created their own review based on their reflection. The students appeared fairly confident and not stressed. 

Click here for this document.

As for me, I was very happy. Since having created the standards and how clear they were for the students, they were also clear to me. Instead of having "Fractions" be the title of the evaluation where before I would have been stressed to create an evaluation that was challenging, reflected the standards, but also would allow the students to show their understanding, having the standards, the creation of the evaluation was easier. I knew exactly what kinds of understanding I was needing to look for. Since there were no "marks" for each question, I could have standards appear in multiple questions, allowing me to see the understanding of my students thinking in diverse problems. At the end I was not trying to determine the "weight" of each question based on the marks out of the total, but now I could create an evaluation that focused on the student showing understanding.

Now that the evaluation has been written, the next part is if the students and parents will understand the feedback. One challenge has been that we don't use percentages, but instead use levels where 3 is meeting the expectations. Parents, struggling to understand how they child is doing, try every which way to convert the level into a percentage, which they understand since it reflects their upbringing. Our the evaluation we have given a level, but also shown where that level came from. This is done through a table at the back outlining the success criteria under each category that the students were provided at the start of the unit. Parents now will be able to see what specific idea/skill/method of explanation their child is working on/proficient/mastered. 

Click here for the evaluation.

Our next step is for the students to complete a reflection upon the return of the evaluation, emailing home this reflection, and then going through the evaluation with their family. We are then asking parents to give us feedback to say if they have a better understanding of their child's understanding and next steps. Hopefully this feedback (in an anonymous survey) will help us identify our next steps for supporting our students and parents to transition into, what we are hoping will be, a growth mindset evaluation process.

Next post will be looking at the parent feedback. I have also been testing out the FreshGrade mark book software and I will also be sharing my thoughts on it.

After reading this, if you have any ideas or recommendations for me, please comment them below. This is a growing stage and all feedback is helpful. 

Assessment: Working towards a "standards based grading"

Learn from your mistakes.

This is the idea that is pushed in my classroom and in the classrooms that I grew up in. The idea that it is important to make mistakes so that you can go back and improve on them. This idea, for the past two years, has made be continuously question the practice that I do in my class around assessment.

As a MS math teacher, I assess students consistently through formative work as well as signature evaluations that are both projects and written "tests". For the projects I was using a rubric, broken down into the categories K/A/T/C, allowing the students to see how to achieve a level 1, 2, 3, or 4. My written tests had marks beside each question, identifying how many of them would go to each category. At the end of the assessment, students would be able to see what level they received in each category... and then move on.

I didn't like this. How was this learning from their mistakes? My questions started to come:

1. After an assessment can my students identify their strengths and challenges based on the curriculum expectations that they were being assessed on or just in the general KATC categories?
2. After an assessment, can my student identify what concept they need to look over again?
3. Why are my parents converting everything into a percentage? Are they unable to identify how their child is doing in their learning?
4. Can my students move into the next unit of study and be given the opportunity to improve on their understanding of a concept AND I have record to show that they have improved?

For each of these questions, my answers were a NO. 

Due to this, I am starting to look at Standards Based Grading... with an Ontario twist. This means that I am making standards that also correspond to the categories. My teaching partner and I have tried quite a few things so far, but we are (for the rest of the year) going straight with the standards. 

Students will get a list of the standards at the start of the next unit. They will see these standards on all of the assessment, and also be given the opportunity to complete a redo/retake of a specific standard that did not go well. 

With this goal in mind I hope that students WILL be able to learn from their mistakes. First they will be able to identify the mistakes, create a review plan and then I can create an assessment that woks best for that student. It also means that a student CAN go back and show understanding when they understand it, not when the project is due. For sure, they will still do that project, but it doesn't mean that in the next unit, they might also include a question/topic that allows them to show an improved way of thinking. 

So far, I am excited. My teaching partner and I are sharing our process so far at the ISOMA conference tomorrow (in Toronto). 

Twitter Chats: Inspirational Weekday Hours

Over the past three weeks I have made an effort to explore Twitter further as my Cohort 21 members have told me about how great a PLC it can be. So I jumped feet first into it by signing up for Twitter deck and found what weekly chats were occurring and which matched my interest. Here is my list.

Monday Night: #MSmathchat
This is the middle school math chat group. I like this group as it is directly linked to my teaching focus. There are great resources for activities, methods of teaching and ideas to engage MS students. Also a great place to meet others that may have a blog with fun resources.

Tuesday Night: #Scichat
This is Science chat with science teachers sharing resources and ideas. The times that I have been on it is not as structured as the other chats, but more of a time that people are around and there if you are wanting to share a challenge or resource.

Wednesday Night: #SBLchat
This chat is the Standards Based Learning group. A big movement in the states, and one that I am interested in exploring. It is a good group to get ideas of how to implement this assessment method in your classroom. I am hoping to bring it in as it matches with Ontario's "Most consistent, Most recent" idea.

Thursday Night: #MSchat
This chat is for Middle School teachers. On my first chat I found a teacher who is doing interesting things with rubrics and student conferencing after projects. This encounter has turned into email exchanges so that I can better understand how she is implementing this strategy. I like this chat as it has all types of individuals connected with the Middle School world so if you have a question or idea, it is a great place to send it and get feedback.

Combining Expectations: Integers, One Step Equations and Translation Vectors

When looking at my curriculum, as I think many other teachers do, thought "How am I going to cover all of this". However, when I started looking through the parts I thought of how each expectation didn't have to be taught separately, but that perhaps if they are taught and explored together they would provide great context and then also the time to think through each of them.

My first attempt at this is exploring translation vectors, integer addition/subtraction and one step equations all in one hit. By doing this, I feel that my students will have longer to look at each concept and also use their strengths in one area to help them in another. I have already seen that my visual students have grasped the addition and subtraction of integers through their translation vectors, better than they would have done if it was taught separately.

I have put below each days goal and the related handout that the students completed (if applicable). My classes next steps are to explore the rest of the transformations on a Cartesian Plane. Through this we will also be looking at composite areas, similar and congruent shapes and two step equations. If you have any ideas of how these can lead into each other please let me know. I have a plan but open to change.

Outline and Resources:

Previously to this we had already explored the transformation terms through dance. Please see the previous post about this exciting activity.

Day 1:

• Explore the Cartesian Plane and how coordinate points are communicated. Translation Vector Intro.
• Resources: Click Here. 

Day 2:

• Translation Vectors Review and Thinking -> Inquiry into integer addition and subtraction.
• Resources: Click Here and Click Here. 

Day 3:

• Determining Translation Vectors through One Step Equations
• All class handout: Click Here. 
• Challenge by Choice
• Green level: Click Here
• Blue Level: Click Here
• Black Level: Click Here

If you are interested in my challenge levels please read my blog post about it. Click Here. 

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.