Wednesday, 23 November 2016

This Week in Math Nation: Collaboration Stations!

For me, teaching has always been the goal and that is pretty clearly reflected in my work experiences. I have spent the last five summers working at camp. I loved being a councillor but I’ve also loved holding more senior positions and being a part of the planning process for both day schedules for campers and training plans for staff.

I’ve worked at two different camps and although the training program is different, there is at least one aspect that is consistent. Both camps trained their staff in a manor that is reflective of a campers experience; the training programs are taught in a way that mimics games, activities and strategies that could be used during a camp day. This is a ‘two for one’ strategy. Not only are staff learning the policies and procedures but they are being provided useful tips for how to make interact with the campers and facilitate a smooth camp day.

One of my favorite parts of teachers college is that it is reflective of this teaching style. Although we are treated as teachers and peers we are also put into the classroom setting and take the perspective of the student. Many of our classes are taught in a way that mirrors how that subject would be taught in a J/I classroom. In my opinion this is beneficial in two ways:

The first is that it allows us to experience exactly what the students experience. We are given the opportunity to see what vocabulary or activities are successful and build our confidence in that subject area versus what may be less helpful or even more harmful.

The second is that it provides us with usable activities or lessons for teaching in our own classroom. We will walk away from each class with a plethora of teaching tricks and tasks for each course we study.

           This week we were given the opportunity to experience co-operative learning/problem solving. We were split into six groups and had to move around the room to co-operatively solve different math problems. There were three types of problems we were expected to solve: a problem using number charts, a problem using toothpicks and a problem using connect-blocks. At each table there were the manipulatives required for one type of problem as well as an envelope that had a set of clues in it (one clue for every group member). Each teacher candidate had to read their clue allowed and then the group was expected to work as a team to solve the problem.
(Example of a connect-blocks station)

This type of learning is beneficial because it forces every student to have a voice within the group. The instructions clearly identified that clues were to be shared orally and could only be placed in the middle once the problem was solved. This prevents potentially introverted or unconfident students from avoiding involvement. Using this type of activity in the classroom would ensure that all students have to be engaged and actively participating. Although learning skills and work habits are not included in math marks, this is also a way to document collaboration skills.

Another positive aspect of this activity is that it gets students up on their feet. For some students this is important because they might struggle to remain seated or still during lessons. Whereas for other students the excitement component could encourage them to be more physically active in the classroom.  
(Example of a toothpick station)

            This is definitely an activity I would be interested in using in my own classroom. As someone who has a more difficult time with math however, I was (at first) slightly nervous about the creation process (ie. Making the problems and creating the clues). However I did some research and found a wonderful article that not only lays out how to organize this type of lesson but it also provides some example problems that could be used. This was encouraging because it made me know that I will always be able to find resources to support and assist with my potential teaching ideas (both in math and other subject areas).

Tuesday, 15 November 2016

There's More to Measurement Than Just Cake!

When I hear measurement, I think baking. No, I’m definitely not your average suzy homemaker (in fact, the exactness of baking actually makes me a little stressed!) But I will still always associate measurements with sugar and flour and measuring cups. I’m not incorrect, the measurement involved in baking still uses metric units and requires mathematical involvement but this week the focus of our lesson and our readings was on the aspect of measurement I often forget about… area and perimeter.

Ah Ha! This week’s moments of excitement

We started today with an open question about making sense of area and perimeter. The question asked us to make two fenced in sections with the same amount of fencing but one section had to have an area that was 6m2 larger than the other. We were trying to create as many examples as we could. There were a few moments about this aspect of the lesson that I was especially excited about.

Reality Check

The first moment of excitement happens in most classes but still makes me more engaged in the lesson every time. Pat’s use of personal anecdotes to create open problems and explain concepts always prevents the question ‘but how is this applicable to real-life?’ which in my opinion is one of the biggest preventers of math appreciation for students. For some reason students have the idea that what they are learning in math is not applicable outside of the classroom and therefore requires less attention. Pat’s use of anecdotes has been a big ‘ah ha’ moment for me as a future math teacher; hopefully by finding my own personal anecdotes to use, I can leap over one of the most common hurtles in math class!

A chance to do my happy dance!
 
My second moment of excitement happened during our independent work time. After successfully completing the question wrong not once but twice (side note: teach your students to ALWAYS read the question properly… maybe even twice so they really have a grasp of what they are trying to do) I finally began to strategize for the actual solution. Somehow, I was able to find a solution. *Insert Happy Dance* I have to admit, this was a pretty proud moment for me; as my previous blogs have explained, I was definitely a student who suffered from mathphobia.

A Note to my Future (Teacher) Self

Now, this is where the problem arose. When given the opportunity to demonstrate my proud moment by explaining my solution, I didn’t know where to start. Whether I blanked because of nerves or I truly couldn’t explain my thoughts it doesn’t matter. This moment provided me with an opportunity for self-reflection. When I begin teaching math I will need to place serious emphasis on learning how to clearly explain myself and therefore I first need to practice breaking down my thoughts and working through my processes step by step.


My mathphobia is depleting more and more throughout this course. I’m realizing that by building some confidence and doing some proper research I will not only be able to get passed my own nervousness associated with math but help my future students by being able to empathize with their feelings and subsequently (hopefully) be able to avoid and debunk the things that make them most uncomfortable. I’ve started doing some research on important tips for math teachers and stumbled upon a list of books that are believed to be ‘must reads’ for math teachers. They definitely won’t teach me everything and they may not teach me a lot but at least I’ll have begun my process to becoming a truly confident math teacher. All research has to start somewhere, right?

Friday, 11 November 2016

Plenty of Polygons: Making Sense of Shapes

As each teacher candidate walked into math this week we received a small Halloween foam sticker. The sticker I received was a small purple cat with a terribly straight tale and an extremely arched back; it was the scaredy cat. Although the way they were handed out was completely random and the stickers were just meant to be a part of our geometry lesson I couldn’t help but giggle at the irony. As each week passes I become more confident in my journey to becoming a math teacher, as though I’m leaving that ‘scaredy cat’ part of me behind me.



The Real Story of the Scaredy Cat
The shapes we were each given were used to split us into groups and review the geometric definitions explained in found in the textbook; such as similar and congruent. As silly as it is (and maybe it’s just me) but I seemed to forget that really, everything is a shape. I never thought of explaining mathematical terms using such fun and silly little items. It was a real ‘ah ha! moment for me! Providing us with the shapes not only made the lesson more engaging and fun but it was another way to put us into groups and force us to work with a new group of people, which is always an important thing to do with young students.


Story Time: The Greedy Triangle
Once again we explored a story as a successful teaching resource for young students, this time talking about geometry. The story follows a shape shifting triangle through his journey exploring polygons with increasing numbers of sides and demonstrates the many places each shape can be found in the real world.


I believe this book would be great for introducing students to thinking about shapes in our world and is a great way to encourage them to start looking for them on their own. If it was my classroom and I was teaching a young junior grade I would preface this story by having students look for shapes in the real world before we read the book and then again after it was read. I also think it is a good introduction to critical thinking. For example, the students could be asked questions about why each shape has particular uses; and this could preface a conversation about how strong triangles are.

Another important aspect of this story is its social implications. Not only is it a helpful resource for teaching geometry but it demonstrates significant ‘life lessons’ that we should constantly be promoting with our students. It endorses respect for our peers and confidence in ourselves all the while teaching geometry.

My Future Classroom:

This week we spent a lot of time learning about classifying different polygons both in the textbook and in class. Once again, it surprised me how much I had forgotten about the different classifications. One of the things I have learned over the last few weeks that I feel to be of the most importance is understanding and remembering mathematical definitions. In order to truly grasp the concepts I feel we need to be able to properly classify all the aspects and use the correct terminology. When I have a classroom I will make sure to take some time near the beginning of each unit to collaboratively create a word/definition wall/chart with my students so they have visuals and definitions to reference throughout the unit.

Thursday, 3 November 2016

Patterns, Expressions, Equations... Oh My!

I have always been pretty confident in my vocabulary and my ability to understand words and place them in the proper context; maybe it’s the English major in me.  However, this math course is entirely popping my word-ego! Twice now I have been completely dumbfounded by the true definition of words I always thought to be synonymous with other math terms.

Number 1: Sum and Product
For my entire math career I have assumed these two words could be interchanged. Maybe this was because of a miscommunication somewhere in my education and maybe its because I just was not paying attention but I always thought they were one and the same. It was not until this year that I learned the word sum was in reference to addition and product to multiplication. Further more, I had absolutely no idea that subtraction and division also had their own ‘total’ words in difference and quotient (and embarrassingly enough it’s taken me about three weeks to remember this one!)

Number 2: Equation and Expression
Again, for some reason I always felt as though these two words were interchangeable. I actually had mostly forgotten about math ‘expressions’ entirely until reading the chapter on ‘patterning and algebra’ in the ‘Making Math Meaningful’ textbook. To be fair, these two are very similar and I can see how students would confuse them. Pertaining to algebraic equations I have now mastered that equations are an expression equal to something else. Therefore equations will have an equal sign, where expressions will not!


©Careccia’s Class Blog
This week one of our instructors told the class that if there is one thing we should take away from our lessons in teachers college it is differentiated instruction, that is, planning lessons and assessments to suit the individual needs of all students. One of the important aspects of differentiated instruction is providing students with choice.

            This week in class we were discussing Patterning and Algebra. The first activity we did had us working with our table groups to sort 16 cards into the 4 patterns they were demonstrating. The patterns were represented through graphs, tables, expressions and models. It was our job to sort the 16 cards into the four matching groups. We also had the opportunity to use 'snap blocks' to give us a concrete example and help visually demonstrate the patterns in a larger form than the model allowed. I really liked this activity because to me, it was an example of differentiated instruction that wasn’t structured towards any particular individual but catered to the possibility of different learning styles. And even though all students would be expected to sort through all four representations, it ensured that there should be a type that would be initially understandable to all learning styles and therefore at least allow everyone to START solving the problem.  For example, I was partial to the Tables or T-charts and used them as my starting point before trying to match them with the other representations.

          I really enjoyed watching the video about three-part lessons. The Brock lesson plan we have been provided is extremely detailed and a little bit daunting. Watching the video about the implementation of lesson plans and seeing the three stages really clarified the information for me. Seeing and hearing the teachers thoughts while going through the process made it much easier to grasp and also demonstrated the positive effects of co-teaching (it's always good to have more than one perspective!)

I did my learning activity presentation this week and have discovered the thing that will be my biggest stepping-stone for teaching – the actual teaching part. Yes, I am aware that standing in front of a group of people is a part of teaching but I never realized how nervous it would make me (mind you, there’s something significantly scarier when its your peers rather than a group of children!). Luckily, Pat showed us a quote beforehand that saved me from letting my feelings about my presentation defeat me...

'Don't cary mistakes with you, place them under your feet and use them as stepping stones' 

I think this may be my new mantra as I work my way through teachers college (and especially my experiences in math!)… after all, this presentation won’t be the first time I feel I could have done better and it definitely won’t be the last! 

Always remember to keep moving forward! :)