The Purpose of Assessment

Clapping Activity: How Assessment Works
This week in math class we started off with a fun activity. Several volunteers went to the front of the room and were divided into to groups. One group were the judges and three other volunteers were the contestants. The first contestant was asked to clap, which she did. The judges then each gave her a grade between 1 and 5. The second contestant was also asked to clap, but was given a slight advantage. The second contestant was given insight to the activity; she knew that she was supposed to clap and saw the contestant before her clap, giving her an idea of what she needs to do. By the time the third contestant was asked to clap, she had seen the other two contestants perform the activity and was given a success criteria that was created by the judges.

The purpose of assessment is to improve student learning. It is an ongoing process and takes place in numerous forms. When we ask students to clap on the spot without giving them information, we are setting them up to fail. When we provide them with examples and a success criteria, however, we are giving them the opportunity to succeed and learn. This activity showed me that putting a student on the spot and asking them to perform an activity, it makes them feel uncomfortable and unconfident. When you explain to a student what they are being asked to do, they can have fun and enjoy learning while being assessed.

Collaborative Activities
We also continued this week with more collaborative activities. In groups of six, we were asked to go around the classroom and solve the various puzzles presented to us. Each member in the group received a clue that they must orally share. This means that each member in the group had to vocally engage in the activity; you couldn't have another student look at your clue. These puzzles varied in difficulty and setup. There were a few activities where we were asked to create a shape using coloured building blocks. There was another activity that asked us to create shapes using toothpicks. There were also games that asked us to find a specific number from 1-100 using the clues we were given. In each game it was not only crucial that each member read out their clue, but that every member was actively participating to make sure that their clue was seen in the activity.

Collaborative activities are a fun way to get students out of their seats and focused on learning, which was specifically math in this case. We have talked about the use of manipulatives throughout this course and continue to see the value in using them within a classroom. I really liked these activities as they took a problem that could be solved by an individual and made the problem solvable only through collaboration. These types of activities help students develop their learning skills and work habits while developing positive peer relationships.

What Makes a Good Assessment Plan?
We also looked at effective assessment plans this week and the characteristics associated with a good assessment plan. A good assessment plan:

• balances the measurement of both mathematics content and processes
• is appropriate for its purpose
• includes a variety of assessment formats
• is aligned with student needs and expectations
• is fair to all students
• is useful in assisting students to assess their own learning
• measures growth over time
• sets high, yet realistic, expectations for students

We also looked at some of the different ways in which assessment data can be gathered:

• portfolios
• performance tasks
• projects
• journals
• observations
• interviews
• homework
• exit passes
• tests and quizzes

One of the main focuses I took from this week's class is the need to step away from old-fashion questions, such as "Does anybody know..." questions. Throughout this course we have been developing open-ended questions where students are free to approach a solution using a variety of strategies. The purpose of a question isn't to see if a student knows the answer, rather to see if a student has a means of getting to that answer. Formulas can be extremely useful in math, but only if a student understands what the formula means. Trying to explain the surface area of a circle to a student can seem difficult without using the

π

r

2 

formula, but it shouldn't. There is a reason why people use that formula and breaking it down is a necessary step to teach students about surface area.

As the video to the above explains, assessment used to be simple. We would give something a try and it was obvious when we did not succeed. It was also obvious when we did. With 21st century learners, assessment has changed greatly. 21st Century learners need to synthesize knowledge, communicate clearly with others, and create solutions to problems that we don't even know exist. In order for students to become learners, rather than just graduates, they need personalized, engaging, and useful feedback on meaningful work. 

I Have...Who Has?

I Have - Who Has?
This week in math class we got to play a fun game called "I have...Who Has?", which can be adapted to virtually any unit of math. As this weeks lesson focused on measurement, the game related to the various terms that are associated with measurements. This game requires a prior knowledge in which students draw upon to answer questions. This game would be most effective at the beginning or end of a lesson. The game start off with a "I have statement" followed by a "Who has" question. Each person is given a card that has an answer and a question. When you hear a question asked that you have the answer to, you stand up and say "I have" and give your answer. You then say "Who has" and pose another question so the game continues. One of my favourite parts about this game is that there is no race to answer quickly. Everyone talks to one another to see what they have as answers and help one another answer the questions. This isn't the first time we have seen this activity being used in our math class and I plan on taking this activity with me wherever I teach as I feel this game can be adapted to all age groups and learning levels.

Measuring Length
While measuring length may seem easy to most adults, it is a concept that young students may struggle with learning. While it is easy for someone to say that a table is 60 centimetres long, the idea of centimetres may not be a familiar one with young students. This weeks math class taught me that measuring length can be broken down. Using nonstandard units as a form of measurement is a great way to introduce the unit to new learners. The picture to the right shows the measurement of a table. If someone told me that the table was 60 centimetres long, I would know what that means. A young student who is just learning how to measure length, however, may have a better understanding of the length if it was described in pencils as opposed to centimetres. Being able to visualize length using everyday items not only helps kinesthetic learners, it helps introduce a foreign concept.

Teaching the Area of a Circle 

This week in math class I had the opportunity to teach my classmates a lesson and receive constructive feedback. The focus of my lesson was the area of a circle, which is a concept that I struggled with in elementary school. The problem was that I was taught to use a specific formula, you know the one, but I wasn't taught what the formula meant. I was familiar with the radius, diameter, and circumference of a circle, but I was told to plug in numbers to the formula in order to generate an answer. The focus of my lesson would be to avoid giving a formula and instead give students an understanding of how a circle could be thought of as a rectangle, as shown in the picture to the right. The use of manipulatives was central to my lesson as I am continuing to understand how important they are for student learning.

Shaping Lives with Geometry

Geometry and the Kinesthetic Learner 
"It is important to note that children's ability to conceptualize shape develops through different stages, and that this development is fostered by each child's experience" (Making Math Meaningful, 395). When teaching students about geometry, there needs to be a physical interaction for students to learn. Students need to physically touch and look at objects to gain a deep understanding of how shapes are formed and notice different aspects of shapes.

Geometrical Terms
Throughout class, we discussed several words and what they mean. Defining these words helped us to identify shapes and classify them. Some of these terms include:
     Similar Shapes - same shapes, but may have a different colour or size
     Congruent Shapes - Shapes are the same and equal
     Symmetry - Two parallel sides are the same, the shape can be folded in half and bot halves mirror                           one another
We also went through the different types of quadrilaterals, some of which include:
     Parallelogram - a quadrilateral with 2 pairs of parallel sides
     Rhombus - A parallelogram with all sides equal in length
     Rectangle - A parallelogram with 4 right angles
     Square - A rectangle with all sides equal in length
   
By allowing the class to collectively define terms and come to an agreement, it allowed us to work together effectively on activities throughout the class. When a common knowledge was shared, we were able to build off of one another's thoughts and complete activities.


The Greedy Triangle
One of the most helpful ways to teach students about shapes is through telling a story. The Greedy Triangle is a story about a triangle who want to gain additional sides to become a different shape. With every additional side, the triangle is able to take on different roles within the shape world. Students are able to see how one side changes a shape and that certain shapes have specific aspects. This book not only goes through various shapes, it also teaches students about individuality as the Triangle goes back to being a triangle because that is what he wants to be.



What did I take away from this week's lesson?
The biggest piece of knowledge that I took away from this week's lesson is the importance of hands on activities and visual representations. Geometry is a very specific topic in math and some students need to see shapes get off the page and take form in their hands. Manipulatives have been a central focus in many of our classes, but I feel that this is a topic in math that absolutely needs them.

Struggle Leads To Growth

Math Can Create Stress

"People who feel math anxious are unable to prevent their stress and worry about doing math from interfering with their ability to perform. Their worry about math so occupies their thoughts, it is hard for them to actually think about math" (Marian Small, Making Math Meaningful). Math is a subject that students struggle with because they are presented with concepts that they might not understand right away. Math is a process where there is a right and wrong answer, requiring hard work and understanding to get the right answer. Students may find math stressful because they know that if they do not get the right answer, they get the wrong answer. This thought is always present while in school, but I would argue is most prominent in a math class. 

How Can I Reduce Stress in a Math Class?

https://goo.gl/rpa3Gx

One of the biggest ways to reduce stress in a math class is to focus on an understanding of math as opposed to following a rigorous set of rules and formulas. Memorization can be extremely problematic in a math class because there are exceptions to rules and not all problems can be solved in the same way. Another way to reduce stress is to remove as many time restrictions as possible. Providing enough time to write a quiz or test is essential to a student's success and allows them to think about questions more clearly and not in a rush. Mistakes are not problematic; they are beneficial. They identify the area of learning that a student needs to focus on and can help in teaching math. It shouldn't be expected of students to learn math concepts immediately. Creating questions where students can approach multiple answers in multiple ways isn't just encouraged, it is necessary for learning. Stress due to math can be minimized by teachers who can identify their students' needs and act upon opportunities that present themselves within the math class.

Patterns and Math

There are several types of patterns in math and are seen on a daily basis. Students start working with patterns in elementary school and will continue working with them as they work their way through high school. A pattern represents an identified regularity. Within a pattern, there is always some element of repetition. The three types of patterns we looked at in class are Repeating Patterns, Growing and Shrinking Patterns, and Recursive Patterns.

Repeating Patterns - In this type of pattern, the shortest part of the pattern is called the core and it repeats itself. Repeating patterns can take on numerous forms and can be used by students to help predict what will happen next.

Growing and Shrinking Patterns - In this type of pattern, growing means the numbers increase in size and shrinking means they decrease in size. Along with number patterns, there can be growing and shrinking shape patterns. 

Recursive Patterns - In this type of pattern, each element in the pattern is defined based on the previous element or elements. The Growing Pattern shown in the picture to the right is an example of a recursive pattern as each element is one square greater then the element before it on the left. 

The Three-part Lesson in Mathematics

We also discussed the concept of a three-part lesson in class. A lesson can be broken up into three parts: Before, During, and After. An important aspect of this lesson is the reflection phase, which takes place between the During part and After part. This type of lesson works in conjunction with assessments and is an effective way to teach students.

Before - In this part of the lesson, students engage in work that draws upon their prior knowledge and what misconceptions they may have. Activating this knowledge helps teachers determine what students know and where to go with their lesson. Allowing students to activate this prior knowledge helps prepare them for the lesson and gets them thinking.

During - In this part of the lesson, students are presented with a problem to solve. Powerful problems allow for a range of solutions or strategies and provide students with choices. During this part of the lesson, students interact with the teacher and themselves to determine what is being asked in the question and how they can go about solving the question. Students can work in pairs or small groups to work collaboratively and reach joint-solutions. During this part, teachers should make sure that all students are working within their zone of proximal development.

Reflection on Student Solutions - The reflection process takes place between part two and three of the lesson. During this process, teachers reflect upon their students' learning process and look at the types of solutions that they presented to the problem. Teachers choose which solutions will be discussed in the After part of the lesson, determining how the solutions are linked and what mathematical language to use/focus on. 

After - This part is often called the consolidation and practice phase of the lesson. In this part of the lesson, the class consolidates through the summary/highlights of the lesson and students learn the big concepts within the lesson. Allowing students to present their solutions to the class helps them to understand their process and allows the class to learn. As a class, students have the opportunity to explain and respond to questions about the ideas found in their own solutions and listen to and question other solutions. Teachers should also allow for independent practice to ensure that students understand concepts outside of working collaboratively.

Growing Patterns: Group Activity

In this weeks class, we looked at an activity aimed towards understanding growing patterns. Working in small groups, we looked at a serious of graphs, formulas, charts, and visual patterns. There were four different patterns and each one aligned itself with one graph, formula, and chart. There was one graph, formula, chart, and pattern that was blank, however, and we were supposed to determine what the missing element looked like. 

Working collaboratively within the group allowed us to solve these blank cards and determine a relationship between the graph, formula, chart, and visual pattern. We also used building blocks to help visually determine what patterns were being used. 

This activity allowed every member of our group to jump in. Some members were more comfortable with the charts while others were comfortable using the formulas. Using each other's strengths allowed us as a group to understand the relationship between the cards and determine which patterns were at play. 

Gizmos

Here are some Gizmos to help teach students the concept of patterns. My favourite Gizmo from this list is Pattern Finder and I think it would be the most effective because of the visuals. Unlike the other two Gizmos, a pattern is not laid out in front of you. Instead, you must follow the frogs to see which lily pads they are jumping to and determine a pattern. 

 

Finding Patterns - Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in the grid.

Pattern Finder - Observe frogs jumping around on coloured lily pads. Find, test, and reason about patterns you see in their jumping

Pattern Flip- In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. The object of the game is to determine which animals are on the face-down cards.