Final Reflection Week 12

 

Final Reflection

We have now come to an end in our first year mathematics course. I must say, I feel like I have come a far way since the first class back in September. I remember entering day one, and we were instructed to write on the Smartboard one word that describes the way we feel towards math. The word I chose was “challenging”. I started becoming really comfortable with mathematics in grades 11 and 12, though I did not major or minor in the subject for my undergraduate degree. Therefore, I was rather nervous entering the course, not remembering formulas and terms. However, it did not take long to get more comfortable with math again. Although there are still some challenges I face in the activities, like the one during week 11 “co-operative group activities,” where we went around in groups of 3 to solve problems at different stations (such as number charts, blocks and stick figure stations).

In addition, I enjoyed the digital word problems that we had to create. It was a fun way to think about math in your everyday life. I really enjoyed looking at my classmates’ word problems, as I found 3 right away that I could relate to. I was happy to see that Shannon had found my math problem relatable as she had commented saying she had just finished painting her basement. It was nice to see that not only could I relate to what my classmates posted, but that there was at least one classmate who could relate to my world problem. Also, although we were instructed that you couldn’t create a word problem on something that has already been done, I found that everyone was very creative and had a wide range of math topics covered. I was really impressed with what the ones I read had come up with for their problems.

Overall, I am very pleased with this course. Leaving this course, I am not afraid in terms of my capability to teach mathematics. Also, I look forward to the class next year, although the setup will be different as it is said to be six weeks rather than twelve. I wish that we could all be in the same class again next year, to see how we have all grown after we teach math in the New Year. It would be interesting to see how comfortable the entire class felt towards it, and how they feel about math after teaching it. Furthermore, I felt that although we were a fairly quiet bunch in terms of classroom discussion aloud, we were given the instruction needed in order to become more comfortable in this subject before our teaching block begins. The Great Games definitely helped along the way because rather than just reading out of the textbook (which was also very helpful and I will never get rid of that textbook), the games helped to make sure I knew what I was doing for that particular unit of math that we were studying that week.

Weekly Report & Reflection Weekly Blog #11

Formative Assessment

This week we covered Geometric art/shapes, as well as a discussion about assessment. I thought that the Geometric Art by Simon Beck were incredible! I have never seen anything like that, as the closest thing to “snow art” I have seen are snow angels and snowmen. These images led into the discussion about geometric art that our mathematics professor, Patricia M, drew in the snow after seeing these images. After discussing drawing the image of a heart in the snow, we did an activity as a class with seeing how many times we could spell heart, using this pyramid image of the lettering of the word “heart”. The following image demonstrates what the activity looks like, and the answer that we came up with as a class.

 

After this activity, we jumped into another activity after reflecting on prizes that we used to collect at the bottom of our cereal boxes. Typically, the cereal companies will have a series of prizes for you to collect. As kids, growing up you always wanted to have at least one of every prize so that you had the entire collection. However, this was hard to come by, as you would receive multiples often. As a class, we tried to figure out how many boxes you would need to purchase, in order to collect all the prizes in the word problem. In our groups, we conducted trial runs with 1 die to see how many cereal boxes we may need to purchase in order to receive one of every prize. My group was able to conduct 5 trials in the allotted time, and the results can be seen below.

My way of thinking about this problem was that if there are 6 prizes, I thought about it in terms of you have a 1 in 6 chance of getting each prize. Therefore, my original thought was that you might get all 6 prizes if you purchased 36 boxes of cereal. However, there is no guaranteed way of knowing the definite answer to a question like this, as Padraic mentioned – different cities may have different prizes, but not all of them.

In addition, we discussed formative assessment. I found this lesson to be very useful as we are about to enter our two week internship, followed by our five week teaching block placement. I learned a lot about the three forms of assessment, as well as the achievement chart for math and descriptive feedback. I plan on keeping notes in the front of my binder from this lesson in regards to the three forms of assessment, as I feel that this lesson will be very helpful when it comes time for me to begin teaching lessons, and providing feedback on student work. I thought descriptive feedback would be any feedback that can lead to student improvement for learning, though I never thought about only providing positive feedback. I like this idea because if you provide students with positive feedback, it builds their confidence and makes them want to continue to do well.

Lastly, we were given time at the end of class to peer-edit the lesson plans that we created in pairs. I found this very useful prior to submitting a final copy. One other pair was able to look over the rough draft of the lesson plan and provide written feedback in the margins to show what could be changed and what needed to be added or expanded on. I found this very helpful as it helps us to improve the lesson plan in a way that a supply would be able to come in and know exactly what is being done that class.

 

Weekly Report & Reflection Weekly Blog #10

Data Management

Mean, Median, Mode, Range

Mean: the average number

Median: the middle number

Mode: the number the occurs most often

Range: the difference between the largest and smallest number 

This week, we covered the data management unit of math. This week our class was in a different environment. We weren't in our normal math classroom where we had access to all our math supplies. This week, math class took place in the computer lab. Our class opened up with stem and leaf plots, based on an estimation of how many oreos fit inside of the jar. Some guesses were repeated (mode), and we were told that our median (based on our guesses) was not accurate to the actual amount of oreos in the jar, which was actually close to one of our outlier guesses. 

 

Evan-Amos. (February 19 2011). Double-Stuf Oreos, by Nabisco. Retrieved from: https://commons.wikimedia.org/wiki/File:Double-Stuf-Oreos.jpg

 

 

In addition, we were told to each select a set of 3 consecutive numbers. From there, we had to determine what our mean was. We repeated the same task for 4, 5, and 6 consecutive numbers. These were my results:

22 + 23 + 24 = 69 / 3 = 23

28 + 29 + 30 + 31 = 118 / 4 = 29.5

22 + 23 + 24 + 25 + 26 = 120 / 5 = 24

28 + 29 + 30 + 31 + 32 + 33 = 183 / 6 = 30.5

Based on my results, I found my mean and median to be the same. I believe that the fact that the numbers were all consecutive is the reason for these results. 

A resource that we learned about this week is Tinkerplots, which is a software made for elementary schools. It allows for us to create statistics with students because it provides us with a lot of the work completed for us. Whether you want to utilize samples or your own findings, you can use this software for both. Some of the resources that this software offers teachers are: 

- instructional movies

- teacher friendly tutorials (teachers can try these out at home before using it as part of their teaching lesson)

- free activities

- free resources

You can utilize this software in the computer lab, and set the students up into sections. If you do not work at an elementary school, you still have access to this software if you purchase it. If you own the software, you can print things to bring into your classroom for your students. The nice thing about this software is that it is a one time fee for life. If you want to access the Website, please visit:

Tinkerplots Software

It is worth noting that you can use this site for other mathematical strands if they deal with patterns. 

Furthermore, one of the math Great Games we were supposed to explore this week was "Probability Games". For anyone who tried to access this game, you too would have been redirected to a different site. If you explore the Website that the link takes you to, you will notice that you can choose games based on what area of math you want to explore, as well as which grade level. If you want to explore this great resource now, or refer back to it for future reference, please visit the following link:

Johnnie's Math Page

 

Lastly, two of the three presentations this week used "Gizmos". I have never used this online resource before but I thoroughly enjoyed it. Thankfully the presenters had everything set up for us so that we didn't have to create an account. This is a resource that I would definitely like to learn how to create lessons on, as a future educator, so that I may utilize this resource in my future math lessons on occasion. 

Weekly Report & Reflection Weekly Blog #9

MEASUREMENT!

Retrieved from: https://pixabay.com/en/inch-tape-tape-measure-measurement-311800/

 

In class this week, we covered the measurement unit. This for me is definitely not my favourite unit in math. We looked at formulas as well as examples provided by our instructor. Our task was to start coming up with lengths and widths in order to find the perimeter and area of these equations. We were to just add them to the table that we had already created based on the teacher’s examples.

 

 

GotCredit. (March 16 2015). Learn. Retrieved from: https://www.flickr.com/photos/jakerust/16846023595/in/photolist-rECgUF-aoMmRf-iZuD4v-egmGV3-55fbhg-cJHGxJ-9iYGTz-5nNSSG-61HzUd-qex9y4-72n24g-a6rwJ7-rbkMWB-d27mBb-4Qou3Y-dZu4aS-66kvP2-p3ErN7-qY13Fs-crGWio-8W35Xo-raCSPN-cEJya3-9mBT1m-6oKrRd-4BErB7-niKRjD-fjyxkZ-4m5ojv-c5hdHC-ihNtgp-bpRSVN-88PM4K-9LXkW-aZhtG4-omuR6Y-dGNUyL-eaVyv6-9Md5QC-gStxEe-qPvbC2-cHF3VJ-eqxQSg-c5hcwm-dSfPUP-jr1bQZ-7J1gDR-9rjHzK-8vHsBS-7FSYt1/

In addition, there were two activities that we did as a class. I really enjoyed the first activity where we were given five slips of paper for each table. The task was to tell the class what you are (i.e. area – where we started at in the task) and then state a definition for a mathematical term, which then would be answered by whoever had the name of the term. The task continued in this manner until everyone had a term to speak, bringing us back to the definition of area by the end of the task. This activity might not be the greatest activity if someone is not an auditory learner. However, it is an engaging way to make sure students are listening to the speaker, while testing their knowledge on definitions and terms.

The second activity we were all told to grab a card at random. Once everyone had a card, and it came time to the activity, we had to find one person in the class who had a card with the same number on it. This task involves inquiry learning. We were to work through the questions on the handout, and try to get as many questions finished in the amount of time we were given. Furthermore, this activity is great for visual learners because we had tools (string, scissors, stamp pad, 2 toilet paper rolls, and measuring tape) in order to help us solve for surface area.

 

 

Dvortygirl. (December 28 2006). Miniature marshmallows, close up. Retrieved from: https://commons.wikimedia.org/wiki/File:Mini_marshmallows_in_bowl.JPG

We then moved on to student presentations. One that stood out for me was the activity that involved marshmallows. This activity was beneficial for me because it allowed me to learn things that I forgot. For instance, we were given two sheets of paper that were the same size. However, we were supposed to make cylinders out of them, by folding them differently (one was short and large, while the other was tall and thin). When determining volume, I assumed they would both hold the same, due to the dimensions of the flattened sheet of paper being equal. However, I quickly learned that the taller and thinner an object is, the less room it has inside to hold something, therefore, the shorter larger one held more marshmallows. I was glad that I got to participate in this activity because that is something I had completely forgotten when dealing with volume, and therefore, this activity served as a great refresher.

 

 

 

Lastly, this week I explored 2 tools on Great Games. The first tool was “Illumination Cube”. This game allows students to look at the flattened image (faces) that make up a cube. Students then can put the cube together to see what it would look like assembled. The task is to find the volume and the surface area of each cube that the tool provides you with.

Illumination Cube

 The second tool was “Shodor’s Interactive Shape Explore”. In comparison to the first tool, I found this tool much simpler to use. I preferred to use this tool to find perimeter and area. I think this is a great tool for students to see a shape, and find the area and perimeter for the shape on the grid. The grid squares are nice and big so that students can physically count the squares to double-check their answers. Give it a try if you haven't already!

Shodor’s Interactive Shape Explore

Weekly Report & Reflection Weekly Blog #8

Geometry and Spatial Sense

This week we covered Geometry and Spatial Sense. What I enjoy about this unit of mathematics is trying to figure out what shapes can come together to build new shapes. We got to work with 7 geometric shapes and we were to try to build other shapes using any or all of the shapes. The challenge was to find up to 7 different ways to build these shapes, which was a fun way to challenge the class, due to the nature of the activity being a challenge.

 

Retrieved from: https://pixabay.com/p-155306/?no_redirect

NCTM Isometric Drawing Tool is one of the Great Games that we were to explore this week. The tool allows you to build 2-D and 3-D shapes. It provides you with tools that allow you to draw figures using cubes, faces and edges. This would be a great resource for younger grades that are being introduced to geometry. The link provides you with clear instructions on what to do on the grid, and which tools can be used for different purposes. If you go to the “Exploration” tab, there are 3 different images you can create using faces or edges. Personally, I preferred using edges when trying to create these shapes. Overall, this is a great beginners resource for students to learn how to create and draw different shapes. You can explore this tool as well by clicking on the following link:

Isometric Drawing Tool

Retrieved from: https://pixabay.com/en/cubes-impossible-geometry-161964/

One of the presenters came up with a Bus Route activity, where students had to find different bus routes to their destination point, as well as spot the parallel and perpendicular lines using the math provided on the handout. This activity serves as a double lesson. While teaching students about parallel and perpendicular lines using real life streets, you are also teaching students how to take different bus routes for those students who may rely on the bus for transportation. The following image is not from the activity, though it resembles part of what we were looking for in terms of parallel and perpendicular lines.

Oran Viriyincy. (October 4 2010). Metro Route 75 Semi-Circle. Retrieved from: https://www.flickr.com/photos/viriyincy/5049887867/in/photolist-8GeZJc-86gLCy-9tXA9R-cA3kB1-f2kaE8-7Gcyum-7xyzQK-aFfVij-qvMwdg-9W23sZ-ahPRR6-diCWTP-diCUdL-diCUmG-48Mr8z-4qobYE-sCgcR-oQwphU-ahPKQR-bnANpX-bs3os6-ahSvfq-ahNPXV-ahQP66-pRaF7A-wiPky-dFUxaG-9yeMNs-dFP8VP-4KevGv-cA3LNS-cA3jkm-8J7tc6-dFUzJG-as8mv6-ahSCyC-5oh8sR-ahPMdk-ahPNPi-yEYhU-sjTw-9yeMJS-9ybNMF-9yeMpJ-9yeMaQ-9ybP2r-9ybPj4-9ybP4D-cPkQj9-cA1uw3

Another activity we worked on at our seats was a Mario Mirrors Handout. I really enjoyed this activity, particularly because I enjoy drawing. However, I completely forgot about the math tool, miras. We had these tools in my elementary school for this unit. It was refreshing seeing different math tools being used as the presentations continue. I thought that this was a fun way to get the audience engaged. We all had to complete Part A which was finding the line of symmetry in the shapes provided. Once that was complete, we could move on to Part B which had 9 Mario images. We were to draw the half of the image that was missing, whether freehand or with the miras. If you got through both sections in a timely fashion, there was a bonus section where you could draw the other half of Mario himself. I like how the presenter acknowledged the fact that some people are right-handed, while others are left-handed, therefore creating handouts that suited both writers. Once the class was finished with their worksheets, the teacher presenter called for volunteers to approach the whiteboard, where they were to complete the mirror image of the incomplete images. The way the presenter set up the whiteboard was as if it was a level in a Mario game. I thought this was engaging for students because many students at the elementary age seem to enjoy playing video games. Therefore, this activity demonstrates how you can make this unit of math fun for students, and have them engaged in the activity.

 

JD Hancock. (July 21 2012). Super Blast Mario. Retrieved from: https://www.flickr.com/photos/jdhancock/7629235266/in/photolist-cCaPR5-et81BA-tcP96D-q9SZza-4FcEsG-4FcEkQ-5S5u7E-dXEcWi-5S5u9Q-7SvZ3M-aVmZ2r-4Hwo86-9RvFkK-qFAsAA-4FcEM5-a4iHmx-5nWUNx-9gztNU-6oTkEy-qNetYS-qLnQNH-pSrhGC-g5GSa-8ZQ4Bz-9j17xH-4HABEj-abh4j6-et81dA-5xviQr-nKP7Jo-a1U5hT-4QWaEQ-5bypdv-pM2Syx-a8K4cL-a2u2Wa-4StQAb-frwyY3-8axuPD-9MNEAs-4dMyLv-c3xpD-33yijA-qHqRCH-4W1UWj-8HaM65-ztKpB-mg5MR6-cPKZyd-ogUi5g