Formative Assessment

Hello fellow math buddies!

This week we covered a lot of ground regarding why and how we formatively assess our students. Though we have covered much of this in our assessment class, it was really nice to hear about it from a math perspective. As I have mentioned before in my blogs, I was not the "best" math student during my elementary and high schools years. However, because of this class, I am pretty confident not only in my math abilities, but in my teaching (math) abilities. Moving forward, these were this past week's activities at a glance...

The first activity that we participated in was a self-assessment. We worked as elbow partners to answer a few questions dealing with multiple math strands and difficulty. After completing the questions, we took up our answers, not in the "traditional" way, but by seeing the answer sheet and marking it ourselves! Personally, I love this type of marking. Not only do the students get to see how/if they went wrong, but they are also able to compare their own processes to that of the correct answer. I think that this is a great tool for students, as it allows them to reflect on their possible mistakes and learn from them! Also, this is amazing for teachers as well, as it gives them more time to plan other lessons and such, as the students are taking the time to mark assessments themselves!

Retrieved from worldartsme.com

Another helpful part of this lesson was being able to determine activities that work for AS, FOR, and OF learning purposes. Regarding AS learning, in my opinion, holding pretests are an excellent way to determine just where your students are in math, and how you can help them to reach their full potential. Pretests almost set up a pathway for the unit, as it shows just exactly what the students know and don't know about a particular subject. I would have loved for my teachers to have given my math classes pretests! I found that all my math lessons worked like clockwork, however, many students were left behind because of how fast the classes were moving! If my teachers had given pretests, I might have felt that my teachers understood my strengths and weaknesses and how to help me with them. Regarding FOR learning, a great way to help students and teachers, is by using a strategy called "My Favourite No". At the beginning of class, students are given a math problem and are asked to solve it anonymously on cue-cards. The students hand their teacher their answers, and they are taken up a group. However, the teacher chooses a card that has the wrong answer, and walks the students through where they might have gone wrong or had difficulty with the problem. Much like our beginning activity, students would be able to see and correct their mistakes, and be able to document it for further reference. OF learning is a summative and formative process that takes as much work as possible of students, and uses it to determine a grade or skill mark (Progress Reports, end of unit projects, Report Cards).

There are many different ways to mark the above learning assessments, however, I'm going to focus on a strategy that I love to use, and loved to see on my reports and projects as a child. What I'm talking about is descriptive feedback. Sure, I loved seeing the marks on my projects or papers (well, only if they were decent marks...), but I also liked reading about how I could improve. I found that I liked constrictive criticism and descriptive feedback on my projects, as it fuelled me to do better for the next one, and helped me to see what else I could do to reach Level 4. As a pre-service teacher, I see that descriptive feedback can be something that helps a student immensely, whether it steers them in the right direction, or if it gives them the extra confidence they need. 

Honestly, I cannot wait to start assessing math homework, quizzes, and projects. I love to see how students' minds works, and how I can help them to understand and solve problems. As I have mentioned before, one of the best things to do regarding assessment ( and any subject in general!) is to keep an open mind and have a positive attitude.

Until the next blog, Happy Math-ing!

Retrieved from home.adelphi.edu.com

Data Management and Probability

Hello all and welcome to/back to my blog!

This week we covered my favourite strand of math: Data Management and Probability! (Ok...it's tied with Geometry for favourite.) As a student, I loved this strand because it was something tangible for me; something that I could actually count. I loved dice, and coins, and spinners; I still do! I felt that by actually having something in my hands, I could learn. I am both a visual and kinaesthetic learner, and so anchor charts and hands-on activities really helped me to grow and learn, both in math and in other subjects. This week's lesson brought back some memories (good ones!), and helped me to visualize how I could help my future students to love this strand as much as I do!

The first activity that I loved during this lesson were the probability starters. I love putting things in order, and pairing them together, so I loved probability starters number one and two. The first starter showed a line of four people, as asked you to make as many different line combinations as possible (hint: it was 24). I enjoyed this activity, as I was able to order them correctly after I wrote them down (hence the visual and kinaesthetic).

Retrieved from transum.org

The second probability starter featured ice cream and how to order double-scoops together. There were six different flavours, and each ice cream cone could only be made once (E.g. Chocolate-Peach and Peach-Chocolate is the same cone!) I enjoyed this activity again, because of the visuals, but also because I really do enjoy ordering things in specific pairings!

Retrieved from transum.org

Another cool idea that I picked up from this lesson (and intend to use!) is the probability field trip to Tim Horton's! As a massive fan of Roll up the Rim, I am all for taking time out of my day during that season to go for a tea. Additionally, and most importantly, I think that this is a great way to show students real-life examples of how probability works in our world on a daily basis. Basically, the point of the trip is to explore theoretical probability (how many times you THINK you'll win/statistics SAY you will win) versus experimental probability (how many times you ACTUALLY win). I find that by introducing students to concepts that they will use/could foresee using in their lives, they are more willing to learn, and more engaged in the learning process. Also, who doesn't love having a nice hot drink on a cold winter day?

Retrieved from smartcanuck.ca

In all, this lesson helped me to think of Data Management and Probability not from a teacher's point of view, but from a student's. I find that it is easier now to remember how I felt about math as a student, and how I solved problems in the past. I looked at this week's lessons as a student, and tried to figure out how I would use these activities in my life (or situations like them). I am so excited to use both my prior knowledge, and my new sense of math-hope to teach my future students about the many strategies they can use to help make not only Data Management and Probability easy for them, but math in general as well!

Measurement!

This week was very important (and nerve-wracking) for me, as I had to present my curriculum learning presentation to the class. Though I have basically been on stage for my entire life, and have no problem speaking (and singing) in front of large audiences, I was completely freaked out about teaching math to my peers. What if I wasn't good enough? What if the students laughed at me!? If you had asked me to sing a piece in Italian, no problem. But present math? That's another story.

Our lesson this week focused on the perimeter and area of a rectangle. Me and my partner handed out work sheets and rulers, explained to the class what perimeter and area are, and sent them on their way to measure out real-life examples of rectangles in the classroom. We devised this lesson from our "Making Math Meaningful" textbook, and related it to the Grade 4 strand of measurement. This is what our handout, and additional practice questions, looked like:

 Retrieved from Personal Collection.

Retrieved from Personal Collection.

Surprisingly, the presentation went pretty well! Since I am pretty talkative anyways, I felt that I was able to, along with my partner, move the presentation and lesson on at a good speed. I felt confident about myself as a future math teacher, and I think that the presentation I gave really helped to put me into the right mindset! This is now how I feel about my math skills: (AKA I've got this!)

Retrieved from Clipart.com

One of the most interesting parts of the overall math lesson on measurement, were the measurement olympics. This is a great way to make sure that all of the students in your class are actively participating in the lesson AND making sure that they understand what they have just learned. This activity promotes collaboration, and really caters to visual and kinaesthetic learners, as it centred around estimation, visual cues, and moving around. The activities that we took part in were discus (throwing paper plates), javelin (throwing straws), shot put (throwing cotton balls) and big foot (measuring who had the biggest foot). Some people got really into the strategies of winning at their task, meanwhile, I just wanted to make sure that I could measure my plate-toss score correctly. Again, this is a great activity to use in the classroom because it gets the students moving and out of their seats. (DPA anyone?)

Retrieved from Pinterest.com

After this week's lesson, as I mentioned before, I felt really good about myself as a math teacher. This lesson inspired me and gave me hope! I really enjoyed using the textbook by Marian Small, and found that it was easy to pick strands from the Ontario Curriculum and relate them to "Making Math Meaningful". I really enjoy going to math class (my grade 10 self is shuddering a bit at that) because I enjoy what I'm learning about! Because of these classes, I have more hope in myself that I can inspire students to enjoy class, and join in to the activities. Math doesn't have to be boring; you as a teacher just have to make sure your lessons are both engaging and enriching for the students.

Geometry and Spatial Sense

I know I said that I loved last week's math lesson (and that's still true!) BUT I loved this week's math lesson even more, because it is the strand that I am most familiar with AND is probably my strongest strand. Geometry makes me happy! I understand shapes, and I understand what to do with them, and how to analyze them! I am a visual learner, and person in general, and this lesson helped me to come up with different strategies to teach my future students geometry. So here's a recap of what went down...

First, we started with a very informative lesson that included toothpick and yummy marshmallows. Our table groups were asked to make 3D shapes, and then we all walked around to see what others had created. I found this to be a great "minds-on" activity, and definitely captured everyone's attention. (Who doesn't like food!?)

My Square-based Pyramid (Personal Collection).

Next, we moved on to a problem-solving activity called "What's my Shape?". In this activity, we were given the number of sides and the number of shapes, and had to come up with what we thought the answers were. The nice thing about this activity is that there could be multiple different answers for the same questions (the fun part was figuring it out!). I really love this activity, as it promotes collaboration among peers, and use students' prior knowledge to help them figure out the answers.

"What's my Shape?" (Personal Collection).

After this activity, we watched James Blunt sing "My Triangle" to the tune of his song "You're Beautiful". I found this video extremely entertaining, and pretty informative when it comes to explaining triangles. Being a music major, I think that by including music into math (and well, anything, really) it is a great way to get students engaged and involved in a lesson, especially if the music is familiar to them.

The next activity we worked on was our "Downtown". In this activity, we were asked to draw a city, and had to include specific shapes that were outlined on the paper we were given. This task is great, because it helps students to visualize 2D shapes, and even helps a little bit with organization, too!

Geometocity (Personal Collection).

We then moved on to teaching geometry through games. Some games that we played with and discussed were Battleship, Dragon Box Elements, Guess my Shape, and Tangrams. To play Battleship, we split our table groups into partners, and drew our own battleship boards. It was the standard game of Battleship, but still fun to play from a geometry point of view, as it helped us to visualize and plot the shapes. Dragon Box Elements is similar to Dragon Box from previous lessons, and helps students to work with shapes, and solve problems through gamification. (Students are learning without even knowing that they are!). Guess my Shape is pretty much the same as Guess Who, except with shapes. Again, our table separated in pairs, one pair chose an envelope with a shape in it, and the other pair had to guess what the shape was by looking at many shapes on the table, and by asking yes or no questions. 

Guess my Shape! (Personal Collection).

One of my favourite things that we worked on, and one of my favourite things from elementary school, were tangrams. Tangrams are outlines of shapes that are made by putting multiple shapes together. As I mentioned before, geometry really works for me, and so do tangrams, as I am able to visualize which shape goes where.

Cat Tangram (Personal Collection).

Before I wrap up my post, I just want to mention the online game that I played this week, and that is the Isometric Drawing Tool. Again, as a visual learner, I really felt that this tool helped me to map out different shapes, and helped me to learn how to rotate/transform them, whether they were 2D or 3D. I would definitely try to use this resource in my own class, and I feel it does help all of the visual and spatial learners out there! 

Like I started my post with, I loved this lesson. I felt that I was extremely engaged, and even wanted to learn more ways of how to teach my students about geometry. I had a lot of fun collaborating with my table group, and plan to use activities and groups like this to help further my own students' learning in the future.

Until next week, Happy Math-ing!

Patterning and Algebra

So...here's the thing. I absolutely loved this week's lesson. I have always been fairly good with patterning, and it's just something that makes sense to me. Visuals are my friends. Here's a breakdown of what happened this week:

We started the lesson with the learning presentation, which was really informative. Sheets were handed out, and not only were we asked to write patterns into a table, but we were asked to draw them as well. I love the idea of this, because it helps students to understand the problem in two different ways (and caters to different learning styles).

After a nice introduction into patterning and algebra, we continued to learn through problem-solving questions. One of my favourite things we worked with this week was the "input-output machine." Again, being a visual person, this way of finding patterns helped and encouraged me, as I was able to "see" how many numbers had been added, multiplied, etc. I think that this is a great resource to use within the school, because students are able to visualize and write the next numbers in the sequence. Additionally, this tactic can help teach students to write a chart out when only visuals are given. (I love that it works both ways!)

Next, we played with tiles. As table groups, we were given rules on a sheet of paper, and were asked to complete at least three terms with our specific rule. The other members in the group were asked to guess the rule based on the pattern of the tiles. We did this activity twice, first with just multiplying the numbers, and second with multiplying and adding the numbers. This is what the activity looked like:

Multiplying by 2. (Personal Collection).

Multiplying by 5, adding 7. (Personal Collection).

The last thing that we focused on during the lesson was playing with the app "Dragon Box". This game helped introduce the concept of algebra to students in a fun and engaging way. The object of this game was to make the Dragon Box disappear by adding a picture to both sides of the screen. If there was the same picture on each side, it would be cancelled out, and the box would be left. (What you do to one side, you must do to the other.) This basically introduces the concept of solving for X, and the students don't even realize it! Like I mentioned before, it is an engaging app, and in my opinion, can be used to introduce students who are either new to or struggling, to the concept of algebra. Additionally, it is a great resource to help students who are great at algebra! It will help them to hone their skills, and stay up to date on algebraic problems.

Overall, this lesson was informative, interesting, and fun! It catered to many different learning styles, and incorporated many concepts to help students stay engaged and motivated while working on patterning and algebra. I hope that I can use some of these tactics in my own future classroom!

Until next week, Happy Math-ing.

How to Think Proportionally!

Hello Everyone!

Today, I will be recapping this week's lesson on Proportional Thinking!

Going into the class, I really had no idea what Proportional Thinking was. After reading the definition for it, I was still confused. However...as we moved into the rest of the lesson, things started to come back...

We started this week's lesson with covering Proportional Thinking in children's literature. The book that was read, "If You Hopped Like a Frog", had to do with Proportional thinking and compared things to each other. Compared....RATIOS! Finally, it started to come back to me. Proportional Thinking is COMPARING things! With hope in my heart, I sat up straight and welcomed the rest of the lesson.

[Online Image]. Retrieved from Amazon.com

Unfortunately, the next part of the lesson was problem solving. For the most part, I've been okay with the concept of problem solving in the past few classes. However, the question that really stumped me was about the distance traveled by a bike and a car, and how they would eventually meet up. I thought I had it. I drew out my number line, and placed the car and bike on it. After a few minutes of struggling to see why these two forms of transportation, I decided I needed help. As it turns out, my number line was almost right, I just forgot to add NEGATIVE INTEGERS into the equation. The problem was, I knew what I wanted to do to get to the correct answer, but I just forgot how to work it out. After about 10 minutes of frustration, I finally solved the problem in two ways. I was happy that I finally understood the question, but I also felt pretty discouraged.

It wasn't until after I solved the problem that I realized I had done an integer problem very similar to this one last week. In fact, I had solved it the same way! For some reason, my brain could not understand the question, simply because I was reading too much into it, and not focusing on the simple aspects. I should have highlighted or underlined the important parts, instead of just staring at the page. There were definitely lessons learned for me this week, both as a student, and as a future teacher. This was the first time that I really thought about how students process questions, and how I as a teacher can help them to understand them and come to the correct conclusion.

After this question, my brain had given up. I had reached the correct answer, but I was confused (not on how I got to the answer, but how I didn't get it in the first place.) We moved onto the final question, which involved measuring a giant's hand with a non-giant's hand. I'm all for open-ended problem solving, but I just could not wrap my head around how to get an answer, any answer!

Dunn, Erin. "Giant Hand."

Overall, though I did enjoy this lesson, I left it frustrated. I wasn't frustrated with the lesson, but with myself. I started to fall back into my old math habits, and it upset me. I know that I have all the necessary tools in my kit to work on the problem, I just need to be patient with myself because they're a bit rusty! I know that I have the ability to solves problems like these, I just need to work a little harder on it.

Hopefully I'll be able to wrap my head around next week's activities. I just need to keep a positive attitude!

Until next week, Happy Math-ing!

Integers!

Hello Everyone!

This week was a pretty fun one in math! I haven't covered the concept of integers in a long time, but somehow, I have managed to retain a bit of knowledge regarding them. It was very exciting for me to be able to quickly figure out the problems and activities, as this rarely happened in any of my high school math classes. So with that, here's a bit of what we covered last week!

The first thing that happened in class was the integer assignment presentation. This presentation was very informative, and a bit of a refresher to those of us who have not worked with integers for a while. This presentation kick started us into our next activity: Integer Football.

Before this class, I had heard about Integer Football, but had never had the chance to play it. In this game, our table groups were split up into teams and given a number line, a die, and a penny. The goal of the game was to make it to the other team's "end zone". When a team rolled the die, that indicated how many spaces they would move. When a team flipped the coin, it told them what direction they would move. (E.g. Heads positive and to the right, Tails negative and to the left). At the beginning of our game, both teams ended up moving in opposite directions, and therefore, scored no points. I think this game is a great introduction to integers, and includes participation from everyone involved! I also liked this game because we learned new things without even realizing it! I believe that in making concepts and ideas relatable, students will learn and remember them so much better than if it were just placed on the whiteboard.

Dunn, Erin. "Integer Football".

The next game that we played was the spinner game. In this game, players had to combine a series of positive and negative integers to create one whole number. To play the game, a player would roll the die, which coincided with how many integers they were able to use to create the whole number, and spin the spinner, which decided what whole number they players would create. I liked this game because it allowed all players to work on and refine their mental math skills together! I think that this is also a great game to use in the classroom, as it promotes teamwork to solve a problem!

Dunn, Erin. "The Spinner Game".

The penultimate activity in this week's lesson was to work on integer word problems, involving Mount Everest, as a group. I'm not going to lie, this made me a bit nervous, as I had to write down my own answer before collaborating as a group. This made me even more nervous as I compared my answer to the other member's answer, and mine was the only one that was different. We all had alternate ways of processing the question, and after much discussion, somehow my answer turned out to be the correct one. I mean, I was hoping it would be, since I was able to explain how I arrived at it, but I was discouraged when I saw the other answers. The lesson learned from this problem is be confident in your answers (and in yourself!), because you may be right! (regardless of what the other answers are).

Dunn, Erin. "Mount Everest Question".

We ended this week's lesson by placing a number line in our interactive notebooks; something that I hope to use in my own future classroom! This is a great visual aid for all students, as it helps them to count and see the integers that they are adding and subtracting.

I enjoyed this lesson immensely, and hope to use these games and activities to spark collaboration, understanding, and confidence in my students!

Until next week, Happy Math-ing!