My Thoughts on Assessment

My experiences with assessment

Growing up, the thought of the word "test" or "exam" used to really scare me. I was always the type to spend many hours studying for a test, thinking I'm prepared, and then completely blank out when it was time to write it. I disliked the pressure of having to answer right or wrong questions to test my knowledge and understanding of a subject. A lot of the time, I felt like I understood the material, but I couldn't always demonstrate my knowledge to the fullest capacity through these assessments.

One of my least favourite subjects in school was math. I always felt that I was forced to solve math problems one way, and one way only. The method that we were taught in class was the answer that the teacher expected on the test. In my math class at Brock, I have learned that there are many different techniques and ways students could use to answer questions, and still get the answer correct. I always wondered why these numerous strategies were never taught to me by my teachers growing up. My perspective on assessments has shifted since beginning my role as a Teacher Candidate.

 Rotas, E. (2011). [Digital image]. Retrieved October 25, 2016, from http://mentorsexpress.blogspot.ca/2015/09/assessment-key-tool-in-21st-century.html 

My current beliefs on assessment

I believe that there shouldn't always be a right or wrong answer, especially when it comes to open-ended assignments. As long as a student can demonstrate their understanding of a subject and back up what they know or provide reasonings for what they have answered, students should be praised for their work. It is important to encourage critical thinking and reflection within a student's work. 

When it comes to assessing elementary school students, I believe that we should be using a variety of assessments instead of relying on quizzes and tests. We should be encouraging students to demonstrate their understanding through experiments, using digital tools and resources for projects and tasks, drama or presentations etc. There are many different ways a teacher could evaluate a student's knowledge of the class material and we should be promoting the diversity of learning. It is important to remember that every student learns and retains information differently. We all possess different types of multiple intelligences that determine what ways we learn best. Educators should always keep this in mind when assessing their students.  

I also believe that providing feedback is important after having assessed students. If we do not provide clear and constructive comments on a student's work, they may not understand or know what the next steps are for improvement. Teachers should always write a detailed comment on a student's evaluation instead of comments such as "Great work" or "Good effort". Feedback gives students motivation to do better, gives a chance to develop their effort, and is a way for continuous learning. Teachers should also keep in mind that when providing feedback to a student, it is important to allow opportunities for improvement after having given the feedback. 

Mean, Median, Mode & Range

Welcome back!

What do your students know about the mean, median, mode, and range of a set of numbers? I found a fun and catchy song that students would enjoy listening to for either a quick review of the terms, or an introduction to the concepts. This video is great because it defines what each term means, and also provides examples and explains how to find them in a set of numbers. Check it out!

Learning how to organize data using mean, median, mode and range can be confusing at times as some students forget what each term means. Once they learn them and practice, they will definitely get the hang of it. I was doing some surfing on Pinterest and found a fun and engaging activity that you can use in your classroom to help your students practice mean, median, mode and range. I found this link on Pinterest, but it originates from a teacher's blog where she shares different activities that she does with her Grade 5 students in her own classroom. 

 M. (2016, January 23). [Digital image]. Retrieved November 27, 2016, from http://crazinessinfifth.blogspot.ca/2016/01/cup-stacking-mean-median-mode-range.html 

This is a fun activity that students will enjoy as they are able to get creative and build their own cup towers. The teacher will divide the students into small groups and provide each group with a set of cups (starting with 50 cups per group). The groups will have 5 minutes to discuss different strategies and practice how they want to stack their cups to build a tower. Then the game begins! The students have 1 minute to build their tower strategically, with as many cups as possible. When time is up, the teacher will collect the data of how many cups each group used, and record it on the board. The next step is to have students calculate the mean, median, mode and range of the data collected and record it on a sheet that is given to them. Once the students are able to complete the first round, they are to begin the second round. In the second round, students are only given 30 cups to build their towers... a little more of a challenge. The students are to repeat the same task as the first round, and collect the data.

This is definitely a great challenge I would have my students complete in my classroom. As they are working in their groups, they will be working collaboratively by sharing strategies, and having math talks!

Let's Measure

Welcome friends!

To start off this week's blog post on the Measurement unit, I would like to share a fun and catchy song that I found on YouTube. I think students who are beginning to learn about the measurement system, or those who just need a refresher would really enjoy it. I can't seem to get it out of my head for the evening !

How would you define measurement? In today's class, my group and I came up with our own interpretation on defining the term. We decided that measurement is the size and/or amount of an object or shape in units. Although this definition may seem broad, this term can be defined in many different ways.

Today's learning activity presenters taught us how to find the area of a rectangle (A = w x l). To go with what we learned, we played an Area Dice Game that quickly became competitive against the two teams in my table.

Image by Yasmine Khaizaran

This game works by each team rolling the dice, and then drawing out the measurements of the shape on the grid. Whichever numbers you land on represent the length and the width. The goal of the game is to have the biggest amount of area covered on the grid. In order to determine who the winner is, the  players would need to use the formula l x w to get the perimeter of the shape, and then add up the total number. The shortcut would be to count out the unit squares inside each shape. It's always good to use the deeper thinking method to keep your mind challenged.

A great tool when learning measurement units is to provide students with a measurement conversion fan. This resource can be found on Teachers Pay Teachers.

https://www.teacherspayteachers.com/Product/Measurement-Conversion-Fans-1186107

This is something that students can make and keep in their binders or their interactive notebooks. It is a great tool that can be used as a quick and easy reference.

Geometric Shapes

Welcome back,

Geometry is a fun unit that you can engage students with many hands-on activities. We played a few games during math class that I am sure I will bring into my practicum and my own classroom.

I enjoyed this week's learning activity covering polygons and 3D shapes. After doing an introductory lesson on what a polygon is and what are the sides, edges and vertices, we had the chance to do a fun activity involving... marshmallows! We were to each create a 3D shape using toothpicks and marshmallows.

Image by Yasmine Khaizaran

I decided to make a pentagonal pyramid (on the left) which includes 5 sides (6 faces, 10 edges and 6 vertices) that we had to label on a worksheet. The polygon on the right was created by Lauren, which she decided to call a triple triangular prism. This was an engaging (not to mention delicious - I did snack on some of the marshmallows!) activity that is a great tool to use when introducing students to polygons. They get the opportunity to shed their creativity in making any kind of polygon they would like, with as many sides and vertices that they choose. After making our own polygons, we did a gallery walk around the class and observed and tried to guess what polygons our colleagues created.

Towards the end of the class, we played a fun game that brought me back to my school days: Battleships. This was one of my favourite games to play in math class as it never really felt like I was learning math. We could spend hours playing because competition amongst the teams always seemed to grow. It is a great game to include when introducing coordinate geometry. Students are able to learn how to graph ordering pairs (with x and y axis extending to negatives and positives). They are practicing how to plot coordinates without even realizing, because the game is that fun!

Image by Yasmine Khaizaran

This game involves each team placing their ships in a way that prevents their opponents from guessing where they are located. Students are to use logic and strategic thinking when trying to guess where the ships are placed on the grid. It is a great way to have students talking math and coordinates!

A computerized version of Battleships can be found on Math Playground. Students can play this game on their iPads or computers at home as well.

Patterns!

Hello!

Patterning is one of my favourite units so I definitely enjoyed this week's math class. My Grade 5 practicum class has just finished working on this unit and I know the students enjoyed it. A month ago, they were assigned an introductory patterning task that they had a lot of fun with. They were put into groups and were asked to come up with 3 different patterns (increasing, decreasing and repeating) using drama and movement; no pen and paper. I could see the students bringing out their creativity and working together collaboratively. It was definitely a fun task to introduce patterning to the class.

In math class this week, we worked on a few different activities. For the first activity, we had to choose a piece of paper from a bag that stated a rule for a pattern. We then had to describe the pattern by stating an input and an output number, and our group members had to guess what the rule is. We each took turns trying to guess each rule. They were really easy at first, but then started to get a little more difficult as there was multiplication and addition involved. You had to multiply and add to the input number in order to get the output number. This became a little more of a challenge.

The second activity we did involved choosing a pattern rule, and then we had to use coloured tiles to represent our pattern to at least input 3. Below is an image of one pattern I created. Please disregard my photoshop skills, as I realized after I took the picture that I added one too many tiles!

Image by Yasmine Khaizaran

This pattern was a little difficult to build as the numbers were increasing a lot, and I was running out of tiles to use! You can see that by multiplying the input by 6 and then adding 3, you end up with a big output number. For the first group of tiles, the input was 1 and the output was 9. The second group: the input was 2 and the output was 15. The final group: the input was 3 and the output was 21. We learned that it is important that students look at patterning with input and output numbers, and to find patterns this way by creating a T chart. We want students to think algebraically and finding a relation horizontally (input to output) instead of just observing the output numbers to find a pattern rule.

After each of us created our own pattern with the coloured tiles, we did a gallery walk around the class and tried to figure out the pattern rules for our classmates creations. Below is a picture of my colleague James' patterned creation. I thought the way he stacked the tiles was cool!

Image by Yasmine Khaizaran

Can you figure out the pattern rules without looking at the little cheat sheet?

Thinking in Proportions

Welcome back!

This week's math class was about proportional thinking or proportional reasoning. I'll be honest; when Sue asked us to pull out our interactive notebooks and jot down anything we know about proportional thinking, I completely blanked out. I did not know what this term meant until Sue explained its definition as well as provided us with examples. As we started to work on some word problems, I was able to become more accustomed to the concept.

Proportional reasoning is a part of the Number Sense and Numeration strand within the curriculum. It is defined as "the ability to compare two things or quantities using multiplicative thinking, and using this in a new situation". The term "multiplicative thinking" threw me off a little, but I was able to understand the main idea of the concept. It's all about the comparison of two quantities, just like ratios.

We worked on different word problems whereby we compared two quantities, and tried to use different methods to solve for the answer (number line, chart/table, graph, algebra etc). We walked around the class to observe all of our colleagues work. It's so interesting to see how everyone has their own method and technique that they prefer to use to solve the same questions!

One interesting problem we worked on with our groups was figuring out the height of a giant using a picture of the giant's hand. We were also able to use any materials we wanted, such as a ruler or a calculator.

Image by Yasmine Khaizaran

After everyone had time to work on the problem, each group shared their technique on how they found their answer. Everyone's method was quite similar. We all started off by measuring our own heights and lengths of our hands, averaged out our measurements, and then used multiplication to figure out what the giant's height may be. Although everyone used similar techniques to solve, we each had different answers in the end. This is because we all have different heights and measurements which would alter what numbers we are using to calculate for the final response. This is such a fun and challenging activity that I will be sure to use in my classroom! My group's final response was 8"11. That's a tall giant!

One of my favourite parts of class is observing how we can use children's literature to learn and teach a math subject. We looked at a book called "If You Hopped Like A Frog" by David M. Shwartz. I found a picture book called "Centipede's 100 Shoes" by Tony Ross that would be another great book to read to the class before introducing the proportional reasoning unit to students. Using children's literature to introduce and talk about a math lesson is a fun way to engage students about learning the topic!

 Ross, T. (2003). Centipede's 100 Shoes. New York: H. Holt. 

Integrating Integers Into the Classroom

Welcome back!

This week's math class was all about integers. This was a unit that I didn't mind too much when I was in school. The rules of adding integers always stuck in my mind. A negative integer plus a negative integer makes a negative integer. A positive integer plus a positive integer makes a positive integer. A positive integer plus a negative integer equals a negative integer. When it comes to subtracting integers, it can become a little tricky. A rule that Sue taught us for subtracting two integers is called KFC.

KFC – Keep the first. Flip the minus sign. Change the second integer to the opposite.

For example, (-4) – (-7) becomes (-4) + 7 which equals 3.

We explored different types of activities that would be interesting to use in the classroom when covering this unit. For one activity called "Stick-it Together", we were provided with a word problem and we had to solve the answer and write it on a sticky note. Once we had our answer, we shared it with the rest of our group members and had to decide on one final solution that we all thought was correct. We then wrote our final solution and answer on a sticky note and stuck it on our worksheet. A lot of us realized that it was a tricky word problem and that we had solved the answer incorrectly because we did not read the question carefully.

Here is an image of our work:

Image by Yasmine Khaizaran

The question reads as follows: Mt.Everest, the highest elevation in Asia, is 29, 028 feet above sea level. The Dead Sea, the lowest elevation, is 1, 312 feet below the sea level. What is the different between these two elevations?

When I read the question, my initial instinct was to subtract the two numbers in order to solve for the answer. I thought because we were looking for the "difference", this meant that I would need to use subtraction. What I didn't realize was that the question states that The Dead Sea is "below elevation", in other words, it is a negative number. The correct way to solve would be to use the KFC method to subtract integers. This would mean keeping the first number (29, 028), flipping the subtraction sign into an addition sign, and then changing the negative number (-1, 312) into a positive number. From there, you would need to add the two positive integers in order to find the answer. As easy as this question was, many of us did not read the question thoroughly through, which caused us to make the slightest error.

This word problem was definitely challenging! It would be a great problem-solving activity to use in the classroom when teaching the integer unit to students.