Formative Assessment- Week 9

This week was all about Formative Assessment! In our textbook, Making Math Meaningful to Canadian Students, K-8 Assessment is defined as, "the gathering of data about student knowledge and or skills, either informally or formally". (page 36) As well, there are three different versions of assessment that we have been learning about in all of our classes, these include: Assessment for Learning, Assessment as Learning, and Assessment of Learning.

Below are two cute and informative videos about formative and summative assessment.



Assessment for Learning, is formative not summative. It can be defined as, "designed primarily to help the teacher tailor instruction to the needs of the needs of the student." (page 36)  This type of assessment is designed to give teachers information so that they can modify and differentiate teaching and learning activities. Teachers must provide feedback so students can advance their learning. Assessment for learning is done all the time through LISTENING!

Assessment as Learning, is a form of assessment for learning. It can be defined as, "focuses on the importance of students thinking about their own performance and learning from it." (page 36) This type of assessment involves metacognition for students. The assessment is the learning and allowing students to improve their learning when the teacher provides examples.

Assessment of Learning, has more than one purpose. It can be defined as, "designed to inform a variety of stakeholders about what a student's knowledge and skills are at a particular point in time." (page 36) Assessment of learning provides the basis of what is reported to parents and school officials. This type of assessment does not have to be only at the end of the course. Assessment of learning is used to confirm what students know and if they have achieved the curriculum expectations.

Chapter three of our math textbook is filled with information about assessment and evaluation, different ways in which we can assess and evaluate our students, different tools to use, strategies, plans and examples for how a teacher should assess students in regards to math. Pat taught us some key ideas about assessment this week that are vital for any teacher.

As we walked into math class this week Pat let each student pick a popsicle stick. We were asked to get into groups of six with students who had popsicle sticks numbered 1-6. Therefore, this activity allowed us to have some choice to pick our groups but not total control over our groups because we had to find students who had popsicle sticks numbered 1-6. I like this idea for creating groups because it allows students to go outside their normal comfort zones/groups that they always choose.

The objective of this activity was to move around with your group of 6 from station to station and complete the activities. At each table groups were tasked with completing the different math activities by using the clues provided. Each student had their own clue and therefore everyone was needed and had a part to play in order to work together and solve the problem. Thus, no matter how students feel about participation and math every student has to provide their clue. We were allowed to share the clue verbally but could not give it to our group members.

Furthermore, each activity center had different manipulatives that our groups had to use to solve the problem. For example, one center had toothpicks, one had a hundred chart, and one had linking cubes. Below are pictures that I took from the different activity centers.

Courtney Helt, 2016

Courtney Helt, 2016

Courtney Helt, 2016

As well, in class we did a clapping activity to show the importance of discussing learning goals, success criteria and climate. Students need to know what is expected of them. For example, the first person clapped and there was no criteria as to how the student should clap or what expectations the teacher had. As each person clapped they received more feedback and criteria and therefore they did better. Thus, it is important that we involve our students in their own formative assessment. It is proven that there will be greater positive results when students take part in their own goal setting.

ASK QUESTIONS STUDENTS CAN ANSWER!!

The Fundamental Purpose of Assessment & Evaluation in math class is to IMPROVE STUDENT LEARNING!

The Keys to Student Success for Assessments:
1. Give students feedback all the time!
2. Monitor progress- gather evidence in a variety of forms to illustrate student's learning & growth
3. Teach in a cyclical way
4. Encourage students to take responsibility for their learning
5. Keep assessment simple = small # of learning goals

As well, we discussed the importance that Descriptive Feedback has for students. Below is a picture of  what is Descriptive Feedback and how it can help students to improve and move a student one step further. There are three things to keep in mind when it comes to providing effective descriptive feedback. 1. List the strengths/assets of the solution. 2. Wonderings- I wonder why you did this? I wonder if you can go further? 3. Challenges/ Fragile Concepts - Next steps- SPECIFICALLY what they need to focus on.

Courtney Helt, 2016

In conclusion, the main idea I took away from this week is that students can be assessed in a variety of ways, for a variety of activities, constantly. The reason for Assessment is to IMPROVE STUDENT LEARNING! To make Assessment successful for students, BE CLEAR ABOUT THE PURPOSE OF EACH ASSESSMENT ACTIVITY!

Cheers, Courtney!

Measurement -Week 8

Teaching Elementary Mathematics, TeacherVision.com. Picture. [Online Image] Google.

This past week was all about Measurement! In our textbook, Making Math Meaningful, measurement is defined as, "the process of assigning a qualitative or quantitative description of size to an object based on a particular attribute."(page 411) Specifically this week we looked at measuring area and perimeter of certain shapes. Our opening activity was an excellent game called, "I have... who has..." This game can be used for multiple subjects to test kids on what they already know in a fun and intriguing way. The premise of the game is this, students each have a card. It is titled "I have" and the state the clue on it and say, "who has?" Then the next person in the class who has the answer to that card states what they have and their clue. For example, "I have, an equilateral triangle. Who has, a shape with six closed equal sides in length?" Someone would answer, "I have a hexagon, who has..." and the game goes on until everyone in the class has stated their clue and the answer and it all goes back to the beginning.

This game is terrific because it allows students to think on their feet and they have to use critical thinking skills for understanding what the question is asking them and to be aware of what questions are being asked in order to answer appropriately. As well, students can work with their table mates to try and figure out the answer to their questions. This game helps students to overcome their math-phobia as well as creates a challenge in which students will be successful. This game went very smoothly with our class and everyone thoroughly enjoyed it. I could see myself using this game in my grade 8 class to review with students certain concepts that they carried over from grade 7 or to quiz the class on certain terms.

Following this opening activity Pat started off a problem to introduce area and perimeter to the class. She presented a  very open ended question that relates to herself as well as her students. The question had a problem involving rabbits, cages and Pat's precious vegetables. Every year in the Fall, Pat changes up her garden. She gathers all the fencing that was used to keep the rabbits out of the cages and creates a plan for next years garden. She asks her family for help, mainly her competitive brothers to try and create 2 rectangular cages that use the same amount of fencing but one cage is 6 square metres greater than the other. What could the side lengths be if the sides are whole number values?

As we were solving this problem with our partners Pat reminded us to keep track of what we were solving in order to understand how far we've gone. This is an excellent way for students to see the work they did by showing it. This helps the students to understand either where they went right or where they went wrong. Pat provided us with manipulative blocks as well as whiteboard graph paper.



Courtney Helt 2016

Above you can see the two different ways in which I solved and drew out the gardens. We knew that the perimeter for both gardens had to be even in order to create a rectangle that was 6 units larger. The perimeter for both gardens is equal to 22, but they both have different areas, 24 metres squared and 30 metres squared. We came to this answer after trial and error of drawing different shaped gardens and going through various multiplications.

Garden 1: Perimeter= 22m
-8m x 3m = 24m squared

Garden 2: Perimeter=22m
-6m x 5m = 30m squared

In Making Math Meaningful, there are three stages that teachers go over with students and they apply to both perimeter and area. The stages include:

-Definition/Comparison: "Students begin to learn to define the measurement, and become aware of and apply a process for comparing items."
-Nonstandard Units: "Students continue to define the measurement while they learn to measure with nonstandard units."
-Standard Units: "Students learn to use measurement tools to measure with standard units."
(page 414)

Area and Perimeter Lesson. Picture. [Online Poster] Google.

Lastly, Pat discussed with the class what was involved for a Guided Inquiry Lesson:
-Inquiry Based
-Develop challenging concepts
-Set-up so small groups can proceed independently
-Still need teacher to facilitate
For example, the lesson would take place after a grade 8 class did an inquiry to discover the relationship between diameter and circumference, and between radius and area.

In conclusion, this week I learned that trying new activities that break me out of my math-phobia shell are extremely helpful and rewarding. It is important to remember to take chances and make mistakes. It is also important to remind our students that making mistakes is imperative because they help us grow and change. We learn the best when we are making  mistakes!

Till next week!
Cheers, Courtney!



Geometry & Spatial Sense - Week 7

Geometry Wordle, Picture. [Online Image] Google.

This week was all about the shapes! Geometry and Spatial Sense was probably my favourite unit back in elementary school. I myself am a very visual and concrete learner. Therefore, getting to see what I'm doing through the use of manipulative's and examples in my own hands, is the best style of learning for me. I also believe students, especially in the elementary grades learn math the best and actually comprehend it when using manipulative's.

                      Geometry Refrence, Picture. [Online Image] Google.                 Geometry 2015-2016, Picture. [Online Image] Google.


We started off the lesson by identifying Key Terms. These included:
-Similar: In math it means the same shape but could be different sizes, colours etc. Shapes are similar when, "they have the same shape, with sides in proportion to one another." (Making Math Meaningful, page 371)

Quiz & Worksheet- Similar Shapes in Math. Picture. [Online Worksheet] Google.

-Congruent: In math means equal, colour does not affect this. Shapes are congruent when, "one can be transformed into the other through a series of flips, slides, and or turns." (Making Math Meaningful, page 370) Sides and angles of a shape can also be considered congruent.

BBC: Congruent Shapes. Picture. [Online Image] Google.

****Everything congruent is similar but everything similar is not congruent!****

Pat taught us that engaging the students in an activity that they can relate to will not only create a fun learning environment but the student will also take more away from the lesson and remember what they are learning. This has been a key idea that Pat has been trying to reinforce throughout ALL our math classes!

Another fun activity we did to kick start our symmetry lesson was getting the entire class to stand up, look at each other and try to identify who is symmetrical, and who is not? I could see this working in  a junior to intermediate classroom exceptionally because again, we are involving the students and associating them to their learning by using real-life concepts to relate math.

Face Symmetry of Celebrities. Picture. [Online Image] Google.

Following this we brought reading into our math lesson.... READING! I know, who would have thought that reading a story goes along with math class. Our math textbook, Making Math Meaningful, provides a list of books at the end of each chapter in which teachers can use as resources to help teach their students math in both a fun and informative way. I believe students love to be read to at any age, so by providing a scenario in which the class can be read to but also taught key math ideas is revolutionary. I would have LOVED this when I was in elementary school.

The book we read was called The Greedy Triangle. The book was about a Triangle who was dissatisfied with how many sides he had. Therefore, he went to the shapeshifter to constantly add more and more sides thinking this would make him happy. The poor triangle had so many sides that he ended up loosing his balance and got in a bad accident. As a result of this, the triangle finally realized that he was happy being himself. This book mixed math and children's literature along with moral values into an excellent combination for learning.



The Greedy Triangle. Picture. [Online Image] Google.

Furthermore, this week was the week I did my lesson plan presentation. I chose the topic of symmetry, specifically reflective symmetry of 2-D and 3-D shapes. The line of symmetry is, "when one half of a shape reflects onto the other half across a line." (Making Math Meaningful, page 354) Many shapes can have one or more lines of symmetry because the more sides there are on a regular polygon, the more lines of symmetry there are because the shape is resembling more and more like a circle. (page 354)

Reflective Symmetry: Is also known as reflectional, or mirror symmetry.
In Making Math Meaningful, reflective symmetry is "when one half of the shape is a reflection of the other half." (page 354) Both 2-D and 3-D Shapes can have reflective symmetry.
-2-D Shape: the reflection is across a line.
-3-D Shape: the reflection is across a plane.
-AND BOTH have opposite sides that are mirror images.

BBC Reflection Symmetry. Picture [Online Image] Google

The lesson and activity was designed for a Grade 4 classroom and I conducted it to my associate teacher candidates. I produced a mini lesson about Symmetry to the class, and then read the scenario and task out to my peers. The task was to follow the treasure hunt map by identifying which shapes are: symmetrical, asymmetrical and how many lines of symmetry does each object have. Once completed, the students found the treasure, "leftover Halloween candy". I feel like this activity ran smoothly and that the class enjoyed it.

Before I did my presentation I felt nervous but I did not realize how nervous I actually was until I got up there. I realized I needed to slow my pace when discussing the activity to the class. I talk REALLY fast when I get nervous so it's good to remember to SLOW DOWN! Especially when teaching in the elementary grades, in order to make sure students understand the concepts that you are teaching.

Courtney Helt



Courtney Helt

Geometry is a topic that students can get excited about! If you want to be an inspiring teacher get the students up and moving, provide worksheets and different manipulative's that the students can engage with. Use multi-media, your smart board so students can physically move shapes and identify their properties. There are thousands of fun and interesting ways that a teacher can teach Geometry. Whether you explore Pinterest or online resources, teachers just have to be willing to go outside of their comfort zone and explore the wonderful possibilities in which you can teach math! This will create a fun and inviting learning environment, in which your students will be successful.

 

KEY TAKE HOME MESSAGE: GEOMETRY YOU GOTTA DO IT TO BE SUCCESSFUL!!!!

 

 

Cheers, Courtney!

Patterns and Algebra - Week 6

Morrison, Chantelle. 2015- Term - 1 Maths - Patterns and Algebra. Picture, [Online Image]

Week 6 was all about Patterns and Algebra. Our course textbook states that, "Patterns represent identified regularities." (Making Math Meaningful, page 606) Thus, patterns always have an element of repetition, whether this is the same repetition repeated over and over again or a "transformation," such as adding 1 or subtracting 1. The textbook defines Algebra as, "a way to represent and explain mathematical relationships and to describe and analyze change." (Making Math Meaningful, page 606)


Helt, Courtney 2016.

Our opening activity this week caused my group a massive headache in the beginning. Consequently, as we received greater clarification from Pat we found ourselves on the right track. This activity proved that it is essential for providing students extra detail when explaining a task in order to set them on the right course. I think every group struggled with this activity in the beginning but as we received the scaffolding from Pat, we were victorious!

The activity asked groups to sort the 16 cards into four groups by matching up the model, table, graph an equation. Easy right? Wrong! There were four blank cards that we had to use to complete each expression and this caused us to mess up.

However, learning from our mistakes is a key part of the education system and a part of life. If we never make a mistake we will never learn.

Moreover, in this lesson we learned more about pattern rules. Students were asked to model the equation by using different coloured cube links. These manipulative's provide excellent feedback and understanding for the student as well as the teacher.

Below is a picture of a pattern we were discussing in class. Here we can see that the pattern starts off with 2 red blocks and 1 green. As you go along the pattern 1 green block is added each time. We had to create an equation from this. Our equation was b= total # of blocks, in which we were adding 2 each time and n= the pattern going up by 1 green each time. Thus, b= 1n +2. We guessed the rule by creating a  T- Chart, in which guess was n and t was total. So, starting at 1, the total number = 3, starting at 2 the total number = 6. Therefore our total = 3n. The patterns can be changed, manipulated and made more difficult for students in the higher grades.


Helt, Courtney 2016.

Below is a link to the Three- Part lesson in Mathematics. We had to view this link before last weeks class. It is a great tool that can help students understand how to effectively create a concise 3 part lesson plan.
http://www.curriculum.org/secretariat/coplanning/learning.shtml

As well, here is another great video by Khan Academy that helps to explain math patterns. Khan Academy is a superb tool that all teachers and students should be familiar with.




In conclusion, the key message I took away from this week was the idea to never give up! No matter how hard the work is we should always be encouraged to strive to do more and to be better. As well, both students and teachers should never be scared to make mistakes and get something wrong. No one is perfect! Everyone makes mistakes! Furthermore, it is how we act accordingly to those mistakes, this is what makes us who we are. As a great cartoon and inspirational teacher would say, "It's time to take chances, make mistakes and get messy." - (Mrs. Frizzle, Magic Schoolbus)

Till next week,
Cheers Courtney