Philosophy of Assessment – My philosophy of assessment and evaluation has drastically changed throughout my education degree. At first I thought assessment and evaluation was quizzes and tests, hand-in assignments, and homework checks; however, I now know that there is so much more to it. I believe formative assessment should be happening each and every day and that summative assessment should be happening at the end of each unit. I still believe that unit tests are important because it will allow the teacher to see how well the students are able to apply their knowledge of the mathematical concepts to given questions. Unit tests seem to be overwhelming for some students because they believe that it is the be-all-end-all of the unit; however, if I am constantly doing formative assessments throughout the unit the students should feel more confident when reaching the unit test. I believe the types of assessment should vary and that students should be allowed to assess themselves, as well as their peers. I believe there should be a balance between assessment in group activities and individual assessment, Throughout pre-internship I placed a great deal of value on the inquiry approach which allowed my students to work in groups as much as they could. Since most things were done in groups, it was difficult for me to assess students on the mathematical abilities individually. I also believe that students should not all be assessed in the same way, and that it is important to make adaptations to the assessment for students who need it.
Assessment and Evaluation in the Field – Throughout my pre-internship I focused on including assessment into every lesson. My coop was one who wanted to have some type of mark in every few days for the students; however, even though there was a mark associated with the assessment, it wasn’t necessarily going to be included in the final grade.
Formative Assessment Used:
Questioning: Questioning was a huge part of my formative assessment. Questioning took place every day and I used this strategy to help me see where the students were at and to see if the students were able to answer the questions I asked them. When I asked questions I would usually get the same three students answering them; however, as time went on more and more students were confident in themselves and they answered the questions. I would also use the questioning strategy when I was helping students individually at their desks. If they weren’t confident in answering or if they didn’t know how to answer, I would go back a step and double check to make sure they understand the first step before moving on to the second step. Even though I was not able to formatively assess all students using the questioning strategy, I believe it still helped me get a good sense of where most students were at in their learning.
Observations: Observations is another assessment strategy that I used every day during my three week block. This assessment strategy was especially important when I did group work with the students because I needed to see which students were participating in the group activity and which students were not. When I noticed students weren’t participating, I began to assign roles for each student in the group; however, sometimes the roles didn’t work out either. There were two students in particular who did not participate in any lesson and who chose to sit there on their own and do their own thing. The one student loved to draw and always sat at her desk and drew things. I took her drawing skills to an advantage and I got her to draw an image, and then enlarge or reduce it by a scale factor. Even though she wasn’t taking part in the actual activity, she was able to still understand the mathematical concepts behind it. For the other student who didn’t participate, I had to sit with him and constantly observe what he was doing. If I was sitting with him, he would do his work, but as soon as I would walk away he would get off task again. It was nice that I co-taught this lesson because I would sit with this student for 15-20 minutes helping them with the activity, while my partner observed the rest of the class. The observation strategy definitely had its advantages throughout my lessons.
Thumbs up, Thumbs down – I used this strategy throughout my Foundations 20 lessons, and it seemed to be successful. When I first used this strategy I didn’t know what I was expecting. Whenever I asked for thumbs up, thumbs down I would only get a couple thumbs up, but because I didn’t know how to go about this assessment strategy I just moved along in my notes, even though I should have went back and re-explained what students weren’t understanding. After discussing this assessment strategy with my coop, we said that if less than half of the class doesn’t have their thumbs up, I should go back in the notes and re-explain concepts. Whenever I wouldn’t get half of the class putting their thumbs up I would call on a student and ask, “what don’t you understand?” or “is there something that I need to clarify?” and they would usually give me an answer. Hearing what the students didn’t understand allowed me to explain concepts more clearly and slowly, and it allowed me to adjust the way I taught the following days.
Peer Assessment – In my Math 9 class the students were working on a building blocks activity where they had to create an object using 5 linking cubes, calculate the surface area of their object, then calculate the surface area of their partner’s object. Once students finished these three steps, they then had to assess their partner’s abilities in calculating the surface area of their object. Some students gave great feedback for their partner and gave suggestions on how to solve for surface area differently. This peer assessment strategy worked extremely well in this class and I am wishing I would have used this strategy more than once.
Entrance slips – Since I focused mainly on inquiry with my Math 9 class, I decided to get the students to solve the surface area of a 3-D shape as they got into class just so I could see where they were at with their understanding of surface area. Since I mostly focused on inquiry and had students calculating the surface area of 3-D objects in groups, I wasn’t sure if they would be able to calculate it individually, which is why I chose to do an entrance slip. Thankfully all students were able to calculate the surface area of the 3-D object.
Concept checks – I was teaching the Ambiguous Case to my Foundations 20 students and I realized that this is an extremely complex topic to cover and that if you make just a little mistake it can impact the rest of the solution. For this reason, I decided to do a concept check on day two of teaching the ambiguous case, just so I could see how the students were doing and what I needed to spend more time on. I gave the students one question to hand in at the end of the class and I was going to assess their work. I gave the students either a 0, a 1, or a 2 based on their solutions, and thankfully all students either received a 1 or a 2. I ended up going over the entire question as a class the following day and highlighted areas of trouble/difficulty that students should acknowledge. This concept check definitely helped me see where the students were struggling and where the students were excelling.
Student explanations – Since I did mostly group work in the Math 9 class, I got students to explain their thought process a lot. Students did a lot of board work in this class so whenever a group solved a question I would randomly choose a group member to explain. Every time we did an activity of this sort I always told the students that each person in their group has to be able to explain the solution, so they might have to teach each other. On the first day I taught this class, I did a board work activity where I wanted students to explain their solutions. Since it was my first day teaching I didn’t know the students so I just expected them all to be able to share. There is one student in this class who is EAL, who is deaf, and who cannot speak English. I didn’t know this at first so I called on him to explain his solutions and he kept saying “I can’t” and I kept trying to encourage him to speak, but he wouldn’t. After the lesson I asked my coop about this student and he explained to me that he is deaf and is an EAL student. I felt so horrible after the fact and I quickly apologized the following day. Once I found out about this student, I made sure not to call on him to verbally explain concepts; however, I did pay extra attention to him during the group work to see if he was participating, which he was. Getting students to explain their solution methods is a great assessment strategy; however, I needed to make adaptations to this strategy along the way.
Summative Assessment Used:
Unit tests – At the end of each unit, students would write a unit test where they would show their knowledge of the mathematical concepts that were presented. I covered two units in Math 9; therefore there were two unit tests, and I covered one unit in Foundations 20; therefore there was one unit test in that class. In my Foundations 20 class, I had 8 students with diagnosed learning disabilities, I had a few students with bad living environments at home, I had a few EAL students, and I had a mix of all other students. Since my class was so diverse, I allowed the students to bring in a formula sheet for the test, and I allowed them extra time if they needed. Allowing the formula sheet and extra time definitely helped some students during the test. For Math 9, I did a verbal test with one student who had trouble writing her thoughts down, but was able to explain everything perfectly when you asked her questions, and I allowed two other students to rewrite the test in their tutorial class. Having these small adaptations for tests allowed students to express their knowledge and understanding in different ways.
Surface Area Around the School – For Math 9, I had the students go around the school and calculate the surface area of random objects. The task was to find an object that has a surface area less than 1000 cm2, less than 20000 cm2, etc. Students worked in groups and had to calculate the surface area of these objects in their worksheet. Since groups all found different objects and finished different amounts of questions, I decided to mark them based on how many questions they did and how many calculations they got right. For example, if a student did 6 out of the 10 questions, they were only marked on the 6 questions that they did. All students were successful with this activity and they all participated in the activity.
Reducing Scale Diagrams – Another activity I did with the Math 9’s was reducing a drawing by a certain scale factor. Students were allowed to choose from 4 different drawings, and they were to reduce that drawing by a scale factor of ½. Since the students were given an entire class period to work on this activity, I decided to take it in for marks. To assess this activity I chose three random lines on their drawing and I calculated to see if it was reduced by a scale factor of ½. If the three lines were accurate, then the student got full marks. I had to adapt this activity for one of the students in this class because he had a hard time understanding what a scale factor actually was. Instead of getting him to reduce the entire drawing by a scale factor ½, I got him to choose a section of the drawing and to focus just on that section. He was assessed the same way as the other students; however, he just had to do less work.
Hand – in Assignment – In my Foundations 20 class, we focused on two topics in the one unit: topic 1 was sine and cosine law for obtuse angles, and topic 2 was the ambiguous case. Since students already had background knowledge on sine and cosine law of acute angles from the previous unit, my coop said the students should be familiar with the topic so I shouldn’t spend much time on it. Since the students were familiar with the topic, I only spent two days on it, and most students seemed comfortable with it. I wanted to assess where the students were at on this topic because they would be using this knowledge when exploring the ambiguous case, so I decided to have students answer a question and hand it in at the end of class. This allowed me to assess where the students were at after spending a couple days on this topic and to see whether or not we need to focus more on this topic when exploring the ambiguous case. Most students were successful in this assignment.
Alignment of field experience and philosophy – I think my assessment and evaluation in the field aligned greatly with my philosophy. I incorporated formative assessment every day, and I found ways to assess students individually and in groups. I did have a summative assessment at the end of each unit, as I had planned; however, I also had an additional summative assessment for each unit, which I did not originally plan. I think my assessment strategies varied throughout my two classes and I made the necessary adaptations to these assessment strategies where need be. Overall, I think my assessment in the field and my philosophy aligned pretty well.
Three Key Learnings –
- Formatively assessing students each day. I learned that formatively assessing students each day is important because it allows you to address the misconceptions that the students have right away, and it allows you to make changes to your lesson plans where needed. I think just quickly observing how students are solving the problem, or just simply asking them questions can give you a rough understanding of how well the students are understanding the concept. When you formatively assess each day you are able to see what topics you need to spend more time on and what topics the students are excelling at.
- Making adaptations to the assessment strategies. I learned that not all students can be assessed the same way and that some students need adaptations when it comes to assessment and evaluation. When we created our assessment plans, we focused on making adaptations for 5 specific learners in the class, and during pre-internship I found myself doing that for the students in my class. I noticed that the way I would assess my student who is deaf and who is EAL is completely different than the way I would assess other students. I noticed that I would make specific adaptations to the assessment for students without even realizing that I was making those adaptations. For example, the student who had trouble understanding scale factor, I allowed him to just pick a section of the drawing instead of the entire drawing. I think it is important to always be making adaptations to assessment and evaluation for students who need it.
- Differentiating assessment and evaluation. I learned that it is important to differentiate the types of assessment you are doing and to not solely have unit tests per se. When students were told they were going to be doing a peer assessment, they were shocked because they had never done that before; however, they were excited because it was something new. It is important to differentiate assessment and evaluation because it helps to assess students from multiple points of view, instead of the traditional unit test as the only form of assessment. Having multiple assessment strategies also helps the teacher notice where the students are successful and where the students need more guidance. For example, if I only used entrance slips and never used student explanations, I wouldn’t be assessing the students equally. Some students might excel in verbally explaining their solutions; however, they might not be successful at writing their solutions down. Since I am differentiating my assessment I am able to assess the students in multiple ways.