I have recently moved my blog to http://mathematicallyteaching.blogspot.ca/. I have included all my past blog posts and I am in the process of ensuring all of the links are working.
I have moved from the WordPress to the Blogger method. Mainly because I am using Google products for all of my school work and having everything in one place made things easier.
Please find me at my new site and with new posts. I hope to continue to collaborate with you in the future!
Ruth
As the flowers are popping out of the ground, and the faint feeling of warm weather is on the horizon, my students are reminding me (both with words and actions) that the school year is coming to a close. This time of year also indicates the end of my Cohort 21 experience. We have our final face to face meeting this Saturday and at this time I will be sharing where I started and how I am finishing my year and my plans.
I have made a Prezi to help summarize my start, path and final goals looking forward. It can be found by clicking here:
http://prezi.com/kxaddpgeykzk/untitled-prezi/?kw=view-kxaddpgeykzk&rc=ref-4388444
I know for me, the Cohort 21 process allowed me to get a kick start and audience for a blog which I have been wanting to start for a few years since using other people’s sites as my key PD when I started teaching. I used other peoples sites as a place to confirm what I felt was a valuable way to teach, engage students and challenge them. Having taught in very isolated places, I needed the outside community to support me in my ideas and help challenge me to improve.
Looking forward, I want to now be apart of the conversation rather than just a listener. This is my biggest take away from the program. I know that I will implement technology in my class, have my students use various resources and share ideas, but I will only improve how I use the new technologies and starteiges by sharing my plans and asking others for feedback.
Richard Bryne from Free Technology for Teachers I feel put it best when he said:
Good teachers have always consulted with other teachers. Twitter didn’t invent professional learning networks, personal learning networks, or professional learning groups.
I want to be a good teacher, and I know that to do so I need to consult with other teachers. The only difference between consulting with teachers in your school and using the internet is the number of people that you can talk to and the feedback that you can get back. I don’t want to wait for a staff meeting to get feedback on my lesson plan for next week, but I need that feedback as soon as possible.
That is how I plan on moving forward. Continue the connections I have made within the Cohort 21 community and outside to be my sounding board and give critique (my students will always be my hardest and honest critic). So thank you to the Cohort 21 community for helping me get started on a longer journey.
Scrolling through my google reader I saw a quick, short post from David Wees asking how do we encourage more questions and the following image:
I am a teacher that believes in inquiry learning and also the power of a student driven project or product, but usually these occur as a summary or summative of learning. However, after my recent experiment of completing the Barbie Bungee activity at the start of my unit and in a non-worksheet format, I have seen and appreciate the power of exploring ideas and concepts through the unknown. This activity had my students exploring the ideas of linear equations without knowing what a linear equation was.
They asked brilliant questions including:
Now, only 9 classes after that activity where students didn’t know what they were looking for, they are now appear to be automatically programed into trying to find a constant rate of change and a starting point (y=mx+b) in each of the problems we look at. As they have gained a greater understanding of their topic they are not asking the insightful questions from before but instead are wondering why I didn’t leave the space on their table of values to include the zero starting value, or if they need to capitalize their variables in an equation. I don’t know if I should be celebrating or concerned.
I also just finished being apart of a webinar by Roger Schank, author of Teaching Minds who shared his view of how he feels that Algebra’s sole purpose is as a method to easily test students, and make benchmarks for university entrance exams. He feels that the multiple steps and multiple areas to have an error do not benefit a student, but only the adults and institutions who require an easy way to grade and place students by how they solve for a variable or express a pattern in the appropriate standard formula.
I know that my students participating in Barbie Bungee activity didn’t need to know the point-slope form or y-intercept form in order create a table, graph the data and find a pattern but they did it anyways. I also know that they used their algebra skills to create a formula or relationship to determine how many elastics they needed to use, all with levels of success. All of this great learning happened, but was followed up with 9 in class days to ensure that they understood what slope meant, how to calculate it in the 3 ways it could be presented in a standard question and how it connects to a graph of a line.
At the end of the day, I am left questioning… do my students know more now that they have been provided the vocabulary and structure to work with linear relations, or have I put a stop on their creative application of the concepts. As a class we will be doing more STEM-like activities and I will be looking to see what my students go to first as their method to solve these new challenges. Will they begin by breaking down the big problem into smaller ones? Will they play with the materials and ask questions to determine if they can find any pattern? Or will they think in what way a linear pattern could be created and what the start and change values should be. Will their questioning level increase or have they reached a level of understanding where they have no desire to explore and think through the problems thoroughly.
I am a “no-textbook” teacher. I feel that as a teacher it is my job to understand my students and then develop the classroom materials, activities and practice questions that are reflective of where they are in their progress and understanding. A textbook does not allow this flexibility and uses terms that may not make sense or encourage a student to take ownership over their understanding.
However, after spending the past few years not using a textbook I was wondering if my students were missing any specific skills that their textbook reading counterparts were gaining. But then it hit me, they were not able to develop the skill of reading and understanding a mathematical text. Everything I had created was based on what they had previously learned and was all hands on or discussion based. At no point were they being asked to read and explore a text that was developed for the purpose of being another resources for them to use. So I decided to have a literacy day in my math class.
After looking through the Math and Literacy materials created by the OAME I created a template that I felt would guide my students through their first textbook based reading. My goal was to have the students learn how to read a textbook or resource by first scanning headings, identifying words they already knew and making some judgments about what material they would be reading about. I asked them to use a chunking method to break up their reading and guide their notes. They use the worksheet that I have linked to here.
As a class we have already looked at slope, but by using the counting method using the rise/run – right triangle start. I photocopied a chapter from a textbook that explore the concept of slope through examples, explanations and a summary of key concepts. Their goal was to take notes using the guided worksheet provided and then assess their understanding by completing 12 questions that had been placed around the room as different stations. They could only use their notes to answer each one.
I was amazed with the positive feedback that I got from the class. They all, contrary to what I thought, went straight into the reading portion and followed the guided steps on their own. I did create a mini “book club” of students that I felt may need more support to go through the process with me, but they became independent after only a slight nudge in the right direction. Since they were able to move onto the 12 stations at their own pace, no one felt rushed or that it was a test. In the end of it all they asked that we could do this activity again at some point in the future, all identifying it as a skill that they feel is necessary for them to have but something they have not had the opportunity to practice.
As a math teacher I realize that I don’t prepare my students in how to read a mathematical text. We go over how to read and decipher word problems, but never the additional resources that are available to them as students. How can I expect my students to become the independent learners if they are unable to use the online and print resources available with any success. As my teaching practice is mainly based on inquiry and hands on activities and group discussion, I have cut the literacy aspect from my curriculum without noticing. How can I expect my students to learn how to read a math text in their English class? As a Grade 8 they won’t make those connections on their own, but be provided with adequate guidance to do so.
Moving forward, I want to do this activity again after we have learned another key concept. I plan to use another textbook so that my students can see a variety of printed sources and next time focus on how to properly read and learn from the examples in the text. In our first attempt I saw that they were unable to properly read and learn from the examples.
I found it interesting to see that with a change in teaching philosophy (no-textbook and inquiry), my students had challenges with skills I took for granted in my textbook based education. What else am I assuming they must be able to do that without practice or direct instruction they are finding more difficult. Next challenge is checking their answers with those posted in the classroom.
Over the past 3 days, my Grade 8 class have been working through the popular Barbie Bungee activity. However, as I have shared in my previous post, they did it without any worksheets or guidelines. It was very coincidental that John Golden of mathhombre wrote a post challenging the worksheet approach of the activity and if an unstructured method would be more beneficial. So after 3 days and the big drops completed, I am writing the results of this first time attempt to the activity and doing it in this manner.
To start off, this activity was used as an introduction to linear relations. The goal of spending 3 days on this activity was to allow the students to generate a solution that without realizing it took into account the rate of change, independent and dependent variables, data collection and organization of data. They will compare their methods and solutions by posting them in the room. As we move through the unit the students and I will point out that they already know many of the new concepts. For example, pointing out that they already know how to calculate the rate of change, but only called it the number of centimeters each rubber band would stretch. I was worried that this final goal would not be possible due to students creating guess and check methods and estimating rather than using the necessary data. I also worried that they had no place to start, or could determine that they needed to do test trials or even consider the height of the Barbie. However, I let go and they struggled, but also came out with valuable results.
The first day was just a day of struggling (or teacher terms of practicing rigor). Given a Barbie, ruler, meter stick and 10 rubber bands my students struggled in where to start, understanding what the goal was and how they could actually get there. This was also the day of deciding what factors were important to measure. Some groups were unmotivated to do anything and decided that finding just how far 10 rubber bands would take the Barbie would be enough. I had prepared a list of probing questions and a worksheet just in case. I only gave the worksheet to 3 out of the 24 groups, but at the end of the day it was in the recycling bin as well. The level of struggle differed between classes (I teach 4 grade 8 classes of 22 students). There were some that didn’t know where to start to others that were debating the need to measure the weight of the barbie and wanting to determine how gravity was affecting the stretch. To allow for these great discussions I now know that groups needed to be small, no larger than 3 people and with something to get them started.
To get everyone started there were guidelines to create a shared document using Google Docs and also to pick up the necessary materials. Each group identified a group leader for these tasks. By doing this it made it easier for every group to get started and everyone to have a job.
To help guide their discussions and questions I asked them to use a Question Ladder which helped them outline a potential plan of attack. By the end of the day, all but three of the 24 groups had an idea of what was going on and a plan. At the end of the day I did go home wondering if this was going to be a long few days. If I had given them the outlined instructions I would have known what step they were on and no one would have been off track, but it wouldn’t have allowed for the insight found on day 2.
Day 2 was the test drop day. By giving the groups a test height to work from also provided the struggling groups a goal and motivation. They were told the height at the start of the class and told that they could go to the drop site as many times as they wanted to test their method. To leave the room and test their method they needed to complete a proposal that had them describe their reasoning behind the number of rubber bands and also the evidence to back this up. This day was the magic day. Students left the room excited to test their ideas and methods, to return shocked that either their Barbie crashed to the floor or didn’t come close. They headed back to the drawing board to identify what they felt was the issue and come up with a new plan or make changes to their old one. Groups came back into the room sharing how close or far they had got. By doing this the groups not only engaged in friendly competition, but also they were sharing with the other groups that it was possible to get close and at least one method worked. Since no one new each others methods or plans, everyone took ownership and pride over their Barbie and calculations. Groups went back two or three times to the test drop to alter their proposals. Each time they returned to the test drop area they needed to create a new proposal and explanation using data. This made the “just add a few” or “take a few off” not an option since they needed data as evidence to back it up. By the end of the day students came back being within 2 centimeters of the floor and ready to move on. There were groups that struggled, but did not stop. They also were motivated to make changes and improve.
Day 3 looked much like day 2. The class came in, excited and eager to know their final height. The proposals from the previous day were handed out and groups retrieved their barbies. I wrote the final height on the board and handed out their final blank proposal sheets. They hurriedly got to work, writing out their methods and completing the calculations and collecting their rubber bands. I set a clock on the board indicating when the drop time would occur. The energy in the room was great as each group felt that they could be the closest to the floor. At the end of it all, the groups were working together to divide up the responsibilities and go to the drop zone. It was a great period.
At the end of it all, I had Barbie’s be as far away as 1.5 meters to multiple coming under the 5 centimeter goal. The final group that won was about 1-2 centimeters from the floor.
The next day (Day 4) I had the girls compare their methods, make a table of values and graph their work. The goal with this was to identify that the methods each group took were very similar, but the cause for differences resulted in how precise they collected their original data. The scatter plots of the data and showed that there was a relationship between the number of rubber bands and the distance dropped. It was at this point that I introduced the linear relations unit, the goal of collecting data and making an equation to represent that data. I also explained to them that this could have been a final test or assessment at the end of the unit and that they all have the skills necessary to do well in the unit. The goal moving forward is to ensure that they understand how the math relates to the data and the vocabulary that we use to describe it.
Looking forward, I would do this activity again next year as the introduction. Since the last day, the students have had no challenges grasping the concepts and demonstrating a good understanding of slope and rate of change. We will be preforming many more of these non-structured experiments throughout the unit and it will be interesting to see what they learned and will improve on each time.
For my IEP students I feel that they would have done better in this type of activity than in a structured one, contrary to my Spec Ed. training. I think that by giving more structure and steps, students can see it as being more places that they could mess up on and feel that they can not continue without the support of a teacher. In this method it looked like just one problem that I only had to give them support at the start and the rest was just a continuation of this.
If you have other great activities for linear relations I would love to hear of them and try them out in a similar manner. I also want to improve on how I am using the results of the activity moving forward. We did the Day 4 summary, but as we have gone ahead, I am finding it challenging to see how I can connect the material back to the activity without the standard “Look, rate of change is just like the number of elastics”. This might be the extent to it, but any suggestions would be great!
After completing day 1 of the infamous Barbie Bungee activity I look on my twitter to see the the following tweet from @ddmeyer:
How many different ways can a popular lesson (Barbie Bungee) go wrong? Extremely provocative post from @mathhombre. bit.ly/ULssnB
— Dan Meyer (@ddmeyer) February 2, 2013
Even though it is only Day 1 of the experience of our 3 day activity, I want to respond to @mathhombre and share what is happening in my Grade 8 class.
Goal:
In 3 math classes, you and your bungee company will take your first customer to the drop point, letting them fall over the side and experiencing the most exhilarating moment of their plastic doll life. Your job is to determine the right length of the bungee cord that will create the best fall. Good Luck!
With only the above goal, my class has started their 3 day (no worksheet) activity to get their Barbie closest to the floor. The students were given only two things to guide them. One is the outline of what is happening and the other is a graphic organizer to help them break down their large question into smaller, simpler ones that they are able to answer. Divided into groups of 3 or 4 with a barbie, ruler, meter stick and 10 rubber bands they have a day to create a plan that will help them determine how many rubber bands they will need to create the best fall for their barbie. As explained in the outline, they have no idea what that height is until the drop day and they aren’t allowed to drop their barbie if they don’t have a logical and well thought out explanation that includes data to support their ideas. To help those that may get stuck I created scaffolding questions that could be given depending where they were being challenged and needing support. I also created a worksheet just in case groups became too lost and frustrated that the overall goal was not being met.
The three days are broken down as follows:
Day 1:
Day 2:
Day 3:
Drop Day
My students will test their ideas and are required to write a proposal on the test drop day, alter their plans accordingly and drop them next Wednesday. After this we will be sharing how each group created their plan and explain their method with the class. My hope is that each group will write out their plans/formulas/calculations/tables on chart paper and post them around the room. As a class they will do a gallery walk to find similarities and differences between their own methods and others. We will also explore which methods worked better than others and ask why that was.
From this I plan on launching into the linear relations unit by associating vocabulary with their methods . For example:
The students bring with them and understanding of percentages, finding patterns and creating an equation to represent a pattern but all within structured standard questions. I am hoping (fingers crossed) that this unstructured activity will give them a starting point to explore and identify what is important in a problem, how to measure it and if there is anyway that they can use their results to make a prediction. We also will be exploring what makes a prediction valid and how to question if it will work in various situations.
I have no idea if any of the groups will save their Barbie’s brains or allow them to have a great fall, but already with the lack of structure of history of working through similar problems they automatically directed themselves to the steps and processes a worksheet would have done. I just feel that a structured worksheet directions would not have made them ask the following questions which were heard today:
I wasn’t planning on posting until the end of the process, but after @mathhombre’s comments, I wanted to share that we are testing this very idea over the next few days.
I hope that you will check in and see how things progress next week. I will also be thinking about where to take the group next and posting their created proposals to show the diversity of what they were able to come up with on their own and without coaching.
This week I was fortunate to be told that Lee Hirsch, director of the film Bully and The Bully Project social campaign was going to speak at St. Clement’s School as apart of their LincWell program. My motivation to go and see him speak was a combination of two interests; storytelling and education. I wanted to know how he was able to capture such a sensitive story with the permission of both the bullies, administration of the school and the victims. As an educator I wanted to see and hear his perspective of what the school and administration both thought they were doing to combat bullying and what they were actually accomplishing. I walked away from the evening with two take away thoughts.
Mr. Hirsch did state that he is not the one with the answers, but just trying to get others to have a conversation about it. His site for Project Bully has many resources, both free and available online for parents, students and educators to go through. He did indicate that he feels there is no magic combination that will improve everyone and every school, but as a community you need to first identify it as a problem and create a solution that is unique and reflects the needs and wants of the community.
Looking ahead I know that I will be thinking of how to make my students feel acknowledged and give them the space to acknowledge the positive actions they are having on each other. Perhaps by giving them the time to show what it means to win in our community, those that are bullied or the bully may start to understand how to positively affect themselves and others. .
After my latest Cohort 21 face to face meeting, I know that my next steps will be to explore the use of Doctopus as an organizational method on Google Drive. I am hoping to use this as a means to help differentiate the students by providing scaffolding to those that need it and challenges to those that are ready.
I have been very fortunate to have a designated period of time with my Grade 8 students focused on taking a pause and reflecting on their past two years of math. The background is it gives the girls time to review before their placement assessment completed at the end of January which has been used to help identify which level of math they should enter in Grade 9. This is because the middle school at BSS uses a reach a-head model that allows students to complete Grade 7, 8 and 9 math courses in their Grade 7/ 8 years and provides them the option of moving into Grade 10 or Grade 9 math in September. Over time this assessment has evolved to become a valuable check-in for both the girls and middle school teachers to see what concepts have stuck, which have become valuable and useful tools and which are needing a second tools. This pause has allowed the girls a chance to have the time without the pressure of grades or new material to seek improvements in their understanding and learn the importance of reviewing past ideas to see what improvements have occurred over time.
With this being my first year teaching Grade 8 at BSS I wanted to use this time to also implement some of my personalization goals stated in my previous post. I wanted my girls to use this time effectively, identifying what they need to review, use resources useful to them and see the result of their personal dedication to improving their understanding. I didn’t want the review to be teacher directed or have students isolating themselves to complete pages and pages of questions.
My plan in a nutshell was to put the students in the driver seat while I sat as a driving instructor. I would be calmly aware of the danger that could happen at any moment with a new driver, but also the thrill of being there when someone finds that independence of directing a vehicle for the first time. But of course you don’t give a new driver the keys right away and hit the highway, but let them practice on side roads and develop their personal driving style.
On the first days back after the holidays the girls collaboratively created “I Can” statements for all of the concepts they had learned over the past two years using a google doc. They did this by looking over all the old notes and assessments, digging deep and using the Bloom’s Taxonomy of questions for math to guide their statements. This process allowed the girls to see all the things they had learned how to do which made a few of them say “I can’t believe we learned all of this!”. This was their start, going through and identifying concepts of confidence and areas of challenge.
Next, a diagnostic. The girls have been using diagnostics throughout the year before any new unit to help them see what they already know, take a guess at ideas and also check their past understanding. They know that diagnostics are for their own learning and used to help show them where they are coming from and also what we are moving towards. And then the review began!
Students came into class with personal goals. They were not waiting for me to tell them what we would be reviewing, but driving the questioning themselves, guided by their personal reflections and diagnostic. As their driving instructor I provided them with a framework to use that focused on concept understanding rather than question completion. They used this framework and graphic organizers found by clicking on the flowchart to help guide their review time and ensure their understanding. Through this process they have shared what they have learned with their peers by creating a group glossary of important terms with urls that help explain ideas further, a list of valuable online resources to help review and understand concepts, creating screencasts on ipads and also designing their own review package of great questions.
At the end of our time, they will take the check in to see their improvement. As their teacher I know that the main outcome that won’t be shown by the results is the ownership the girls now have over their learning. They are not waiting for me to tell them step-by-step how to parallel park, but seeing their peers, websites, analytical skills and also their own creative methods to find answers to questions, and generate new questions to help them move forward.
By having my girls learn these 21st Century Skills when not learning new concepts or with a calculated grade at the end gave them the time and comfort to take the wheel and cruise their first solo test drive. I don’t know if this was done during an assessed unit they would have accepted the independence as readily.
Moving forward I am eager to see how these skills and confidence will transfer into our next unit. Will they be able to identify when they properly understand a concept, find that multiple explanations are important? In the end I do wish that they see me as not the driver of their learning, but just along for the sometimes scary but exciting journey.
As I have stated in my previous posts, I am beginning the process to create a personalized learning environment in my classroom. I felt that over the holidays I would think about how I was going to do this, but unfortunately food, family and the amazing outdoors were too good to pass over and I started into my first week back with the same ideas and challenges that were infront of me in December.
Luckily for me that week back was filled with the ISOMA math conference and a two day math department PD session working with Carmel Schettino. Even though neither of these days were focused on personalized learning classrooms, they did allow me to reflect and consider the benefits of a problem based learning classroom and how this pedagogy could be integrated into the structure that I am hoping to put in place.
An “Ah-Ha” moment came when Carmel showed us a video clip (shown below) of Andrew Wiles, the mathematician who proved Fermat’s Last Theorem.
As you watch the video, Mr. Wiles describes the challenge of working through this great problem as if walking around a mansion in the dark. When hearing this I pictured my students and their experience with math as a similar process. It is no wonder that they prefer a structured classroom where they can identify what they are learning and have the teacher do direct instruction so that they can never feel lost in the dark. However, with current research and the goal for 21st century learning skills in the classroom, direct instruction is no longer wanted. This change to a personalized classroom is encouraging students to gain the skills of perseverance, collaboration and intrinsic motivation. However these skills are not natural to all students and this transition can prove to be more challenging for some than others.
One of the other teachers in the group stated that Andrew Wiles is being paid and is choosing to move through the dark while our students don’t have that choice nor the skills to do so. This was my lightbulb moment and generated a question that may direct my work over the next few months. That question is “What tools do my students need to be able to begin to move through the dark on their own and how do I give them those tools without guding their way?”.
I have now started to look at providing my students with various reflective graphic organizers and suggested maps to help them identify their needs, strengths and what first steps they need to do when faced with a dark room. I have decided to continue to use the Green, Blue and Black levels in my class so that students have the ability to self-select the level of speed and scaffolding they will require to move through the dark. As a class we have already begun creating lists of various online resources that they are able to use to help become more independent learners as well as identify the specific skills and math concepts they have learned so far this year that are now in their toolbox.
By taking the time to ensure that my students understand themselves, their point in understanding and showing them where they can go for clarification other than the teacher, I am hoping that the transition to a personalized classroom will be more like walking through a dark mansion with each of them having a small candle to help them make the choice in which direction to take their next step. 
My next step is to find an online tool that will work well for my students to start creating a map of their skills and concepts. By showing how they are connected to each other, I feel that they will be able to see math as the interconnected web that is necessary to see when working through problems. I am hoping that this tool will allow them to show concept connections, imbed links to websites of interest as well as examples of problems that make the connections between concepts.
If you have any mind mapping software that is free and have some or all of the characteristics above it would be great to hear your suggestions.
