“Blog about it” Entry #5

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My pre-internship experience was one that I will never forget. I was encouraged to try new things and focus on different strategies as time went on. I taught a Math 9 class and a Foundations 20 class, and they were both taught two completely different ways. Even though I was the teacher in both of these classes, the way I taught and the strategies I used differed. I taught Math 9 through an inquiry approach, whereas Foundations 20 was taught through a more direct teaching approach. I learned through pre-internship that no two classes can be taught the same way. When I attempted inquiry in my Foundations 20 class, it failed; however, when I used inquiry in my Math 9 class, the students were engaged and were loving it.

I also had to differentiate my instruction and assessment a lot throughout pre-internship and I had to make adaptations to some of my assessment strategies to fit the students’ needs. Some assessment strategies I used were: (1) observations, (2) peer assessment, (3) entrance slips, (4) hand-in assignments, (5) concept checks, and (6) unit tests. Each one of these assessment strategies allowed me to view where my students were in their learning and what I needed to spend more time while I am teaching. My students loved having these different forms of assessment. When students had to do the peer assessment, I was shocked by the advice I had seen on some of these students’ assessments. Several students gave tips on how to solve the question differently and other students gave great feedback on how their peer was doing.

Inquiry was a strategy that I focused on greatly throughout pre-internship; however, I also realized the importance of direct teaching as well. After attempting and failing at an inquiry lesson in Foundations 20 I turned to direct teaching. My notes were fill in the blank and there were multiple examples in the notes that we went through as a class, and that I got the students to attempt. When I turned to direct teaching I had several students come up to me afterwards and say that they love how I am teaching and how my notes are laid out. I also had students tell me to continue teaching this way because it was easy to follow and they understood each step.

In my Math 9 class that I taught through inquiry, I had some students share with me that this was the first time they have ever learned / understood math, and that this was the first time they have ever excelled in math. Several students mentioned that by doing the hands-on activities they are developing a deeper understanding of the mathematical concepts than they would if it was taught from a direct approach.

In conclusion, I noticed that one teaching approach doesn’t necessarily work for all classes, and that to teach successfully you need to have multiple approaches under your belt.

Demonstration of Learning

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.  

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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.

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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.

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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.

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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.  

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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.

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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 –

  1. 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.
  2. 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.
  3. 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.  

 

Learning Journey Blog – Week 8

This week in class we discussed about numerous topics. I enjoyed when we went into groups and took turns discussing the quote that stood out to us the most on the “8 Takes on Thoughtful Assessment” handout. Having the opportunity to speak freely about a quote for 45 seconds without being interrupted was a great experience; however, sometimes it was difficult to stop what you were saying at the 45 second mark. I also realized that it was quite difficult to not interrupt others when they were sharing their thoughts. I noticed that I would nod and say words, such as “yeah” and “mhmm” as they were speaking so they could see that I was listening to them. At first I almost forgot that we weren’t supposed to interrupt the speaker, and I caught myself starting to speak when another person was speaking and I quickly silenced myself. This is an activity that I find extremely beneficial in the classroom and it reminded me of the “talking circle” strategy. I did some research on talking circles and in this article I discovered that talking circles is a means of sharing and communicating founded by Indigenous Peoples, and is now being used in the classroom setting. In a classroom, talking circles are used the same way as Indigenous Peoples use it outside of school. Desks are moved out of the way, students sit in a welcoming circle, and students take turns talking using a talking stick. According to the article, “Incorporating a talking circle format in the classroom is an effective way of creating a safe environment while allowing students to engage more fully.” Creating a safe environment and encourages students to express themselves are two key aspects in my teaching philosophy, and by using talking circles in my classroom, I believe I can reach these goals.

The other activity I enjoyed and learned a lot from is “Opposites Activity”. This activity encouraged us to think deeply about how we will incorporate assessment practices into our classroom, and compare it to others. It was interesting to see how others people’s views on assessment practices in the mathematics classroom differed from mine. My view on emphasizing recent achievement differed from one my classmates, and we had a strong discussion about why we thought emphasizing recent achievement was or was not important in the classroom and it changed my thought on it. As I was discussing with my peer, this activity started to resemble a debate. Throughout my schooling, I learned that debates can be an effective way of assessing students, if all students are taking part in the activity. According to article “Classroom activities: How to hold a classroom debate” classroom debates can “foster presentation skills, research, teamwork, and public speaking. So if you want to get your students excited about what they are learning, then try holding a classroom debate. Here’s how to get started.” I believe allowing students to practice these skills, while expressing their thoughts towards something they think strongly about will lead them to deep understanding. An interesting mathematics debate idea that was presented to us by Jeremy Sundeen was having students research the pipelines and transportation of oil, and then students had to debate whether they were for or against the use of pipelines to transport oil. While researching, students would be accessing the oil spill rates, the percentage of land that has been destroyed/taken over by pipelines, etc. Even though debates are sometimes difficult to implement, I believe they are a great instructional strategy.

During this last class, I learned several things in regards to sharing and discussing with others, and I plan to implement these strategies into my classroom.

Learning Journey Blog – Week 6

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This week we had several group presentations on their assessment plans, and I learned many new assessment tools that I did not know of beforehand. One assessment tool that showed up a few times was the 3-2-1 assessment tool. I thought this assessment tool was interesting so I decided to dig a little deeper and find out more about it. On the teacher tool kit website I found information that was similar to what was shared in class. After the lesson the students write down three things they learned from the lesson, two things they found interesting/would like to learn more about, and one question they still have about the material. However, one thing of the most important things that was mentioned on this website is that you need to review the students’ responses. As the teacher tool kit website states, “You can use this information to help develop future lessons and determine if some of the material needs to be taught again.” I was shocked by all the assessment tools that were presented in class Wednesday night, and the purposes they all had. Learning about these different assessment tools will definitely help me as I move forward in my education.

The other thing we focused on in Wednesday’s class was course plans. I was never really aware of course plans until this semester where I have been told about them in several classes. It was great to have had some prior knowledge on course plans; however, I still learned many new things. What I have been taught in my EMTH courses is that a course plan is a layout of your outcomes from the curriculum in the order you want to teach them with explanations that connect the outcomes to one another. The course plans that I created in EMTH were mostly teacher focused as it didn’t include any assignments, grades, contact information, materials, dates, or I can statements. Now I have learned that course plans should be student friendly and should include all details that the students would need for the course. The center for teaching and learning at the University or Washington has a page on their website which states how to create a course plan and what should be included in one. Something I found interesting from this website is that when you are creating a course plan you should be asking yourself the following questions:” 1) Who are the students? 2) What do I want students to be able to do? 3) How will I measure students’ abilities?” They also stated that, “by asking yourself these questions at the onset of your course design process you will be able to focus more concretely on learning outcomes”. This is important because you should be focusing on the students’ learning and their learning outcomes as opposed to focusing on how you will squeeze in every bit of information into a short period of time.

Wednesday’s class was full of information that will definitely help me in the future.

Sources:

3-2-1. (n.d.). The teacher tool kit. Retrieved from http://www.theteachertoolkit.com/index.php/tool/3-2-1

Course and syllabus design. (n.d.). The center for teaching and learning: University of Washington. Seattle, WA. Retrieved from http://www.washington.edu/teaching/teaching-resources/preparing-to-teach/designing-your-course-and-syllabus/

 

 

“Blog about it” Entry #4

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“At first I kept longing for someone to just show me what inquiry was.” (p. 454) – Brea

I open with this quote from the article, as this is what I continue to ask as I move along my educational journey; however, as I think of it more and more, I am being shown what inquiry is as I am being taught through it in this course. I am not only being shown what inquiry is, but I am living it as well. We take part in many inquiry processes throughout this course, such as reflecting (blog posts), creating (PSE and TMTI), and participating as students (labs). I noticed that because we are being taught through inquiry I enjoy this course much more, and as Brea shared, “The more we enter into a topic, the more exciting it becomes, it all seems new to me again, it is exciting and alive” (p. 450). When we began the PSE part 2 assignment, I was beyond excited because it was something different and it was something I never experienced before. I have created rubrics before; however, I have never created them for this purpose- which got me intrigued. During the labs we are “in an inquiry-based mathematics classroom, [and we, as the] students take on the role of, and learn how to be, mathematicians” (p.448). This is beneficial because I not only get to experience what it is like to teach through inquiry, but I can see what my students would be experiencing in this type of mathematics classroom.  

The ideas in this article affirm my mathematical beliefs about teaching and learning. Specifically, two of my mathematical beliefs, math is everywhere and all students can learn, directly relate to Brea’s change when “her thinking shifted to a humanistic perspective of mathematics as a living disciple and an inquiry perspective of teaching and learning in which learner-focusedness was central” (p. 456). My mathematical beliefs are highly present throughout this article and I believe the inquiry approach plays an important role in learning mathematics; however, there are still several things I need to learn and many steps I need to take before completely emerging myself into the inquiry process.

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Learning Journey Blog – Week 4

The presentation we had on Wednesday night was something I very much needed at this point in my education. I could have listened to Rod Houk talk about assessment in a mathematics classroom for several hours, and I am wishing we had more time to talk with and learn from him. The way he speaks of assessment in a mathematics classroom is different than how I am being taught in my education mathematics courses. I am being taught to teach my mathematics lessons through inquiry, and nothing but inquiry; however, I still have difficulty understanding how to implement inquiry in mathematics classes, other than Workplace & Apprentice. When I think of teaching a mathematics lesson, I feel overwhelmed because I do not have a clear idea of how to teach it, but after listening to Rod’s presentation, he has made me feel more confident in my teaching abilities.

Rod said that if you are engaged in the material and ready to learn, then your students will be engaged and ready to learn as well. I agree with this fact because when I was in high school, if my teacher wasn’t engaged with the subject, then I wasn’t engaged with subject either, but if my teacher was engaged with the subject, then I was usually engaged with it as well. Jo Boaler talks about teachers who follow the traditional approach, but they also, “ask students great questions, engage them in interesting mathematical inquiries, and give students opportunities to solve problems, not just rehearse standard methods.” (p.39-40). This is something that Rod also mentioned in his presentation – it doesn’t matter which way you teach, all that matters is that you pose really good guiding questions and you engage your students.

I now know that there isn’t only one right way to teach mathematics, and that it can be done in multiple ways. I now know that if I don’t constantly teach through inquiry, I won’t be ruining my students’ futures. I now know that there are many ways to teach mathematics, and what matters the most is your relationship with the students. Rod mentioned that having relationships with your students is important for your students to succeed. When they feel that you want to be there and you want to teach them, then they will begin to want to be there and they will want to be taught.

My high school mathematics teacher was the absolute best. He joked around with us, he shared stories with us, and when I was in AP Calculus, he showed us a movie that related to teaching mathematics, and that movie has since been apart of my educational story. The movie Stand and Deliver has a great message about building relationships with students. It doesn’t matter where you come from, or how you teach, but as long as the relationship with the students is there, and the relationship is positive, then the students can amount to anything.

Rod’s presentation was fantastic, and he gave us many useful tools that I will definitely use in my education classes and in my future teaching careers.

Resources:

Boaler, J. (2015). What’s Math Got To Do With It?: how teachers and parents can transform mathematics learning and inspire success. New York: Viking.

Musca, T. (Producer), & Menéndez, R. (Director). (1988). Stand and Deliver. [Motion Picture]. United States: Warner Bros.

“Blog about it” Entry #3

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Journal writing is the assessment strategy that I became an ‘expert’ on, and I realized that it is beneficial in a mathematics classroom. Typically, journal writing is implemented once a week at the beginning or end of a lesson and students are to write about a given prompt for 10-15 minutes. Through journaling, students improve their problem solving skills, it encourages them to reflect on their mathematical thinking, and it helps the teacher identify misconceptions that the students might have. Below is a table that includes some journal writing prompts that I believe are beneficial.

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Interviews is an assessment strategy that I didn’t know could be implemented into a mathematics classroom. Giving students the opportunity to choose which mathematics topic they want to be interviewed on gives them the confidence to verbally express their knowledge and understanding of the topic, and it allows the teacher to understand how the student thinks mathematically. Through interviews, students will also be “… developing their understandings of the language of mathematics and their ability to use mathematics as a language and representation system.” (SK Ministry of Education, 2010).

Portfolios is an assessment strategy that I believe has many benefits. Students can add mathematics assignments, journal writings, projects, and anything else they find important into their portfolios. When the portfolios are being added to on a weekly basis, students and teacher are able to see the students progress and identify which areas the students excel in and which areas they need more help in.

The assessment strategies that are being used should align with what is being taught and the objective of the lesson. If we only use the same two assessment strategies, it can “limit students’ ability or opportunity to show what they know.” (Davies, 2011). Having a variety of assessment strategies allows students to express their understandings in a variety of ways.

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Learning Journey Blog – Week 2

Prior to ECS 410, I did not know anything about diagnostic assessment, but as I read and learn about it I notice that assessment for learning and diagnostic assessment go hand in hand. Although diagnostic assessment is something you do prior to learning a concept, and assessment for learning is something you do throughout the process of learning, they both aid in gathering information about the students knowledge. When I think of assessment for learning and diagnostic assessment, I think of teachers who “collect information that will inform the teacher’s next teaching steps and the student’s next learning steps.” (p.2)

I began searching for different ways to assess students in a classroom, and I came across an article titled “Seven Practices for Effective Learning”. As I was going through the article, I came across the third practice which was titled “Practice 3: Assess before teaching”. This section of the article related directly to what we have been learning in ECS 410 so far, which is diagnostic assessment. In class we talked a lot about the benefits of diagnostic assessment and how it will help us determine where the students are at in their learning, and where we should make changes and adaptations in our lesson plans to fit the students’ needs based on the diagnostic assessment. The following quote from the article I mentioned above logically states the importance of diagnostic assessment.

Armed with this diagnostic information, a teacher gains greater insight into what to teach, by knowing what skill gaps to address or by skipping material previously mastered; into how to teach, by using grouping options and initiating activities based on preferred learning styles and interests; and into how to connect the content to students’ interests and talents.

                                               – Jay McTighe and Ken O’Connor

Diagnostic assessment was something I never really thought of doing in a mathematics classroom. I figured that if the students were in the class, they would have previous knowledge of the mathematical concepts being presented and if they did not they would just have to pay closer attention. However, I now know that is definitely not the way to teach and that I have to make adaptations to my lessons that will help me teach towards each student. When we had to come up with three diagnostic assessment tools for a grade 9 mathematics outcome in class, I was a bit overwhelmed because all I could think of was giving a pre-test; however, I soon came to realize that there are MANY diagnostic assessment tools that can be used across all subjects.

As I was searching for information related to diagnostic assessment, I came across a slideshow titled “Diagnostic Assessment Ideas”. As I was going through the slide, I noticed that some of these tools were similar to the ones we thought of in class; however, there were a couple new ones that I have not seen before. One of these tools is called “Word Splash”, which is where “students are given key words from the unit of study prior to learning [and] students are to write about their understandings of the words” (slide 14) I think Word Splash is a diagnostic tool that could be implemented across all subject areas, especially mathematics. If I simply put the words, right triangle, hypotenuse, and angles, my students could come up with many ideas of how these words connect. The topic that I would want them to discover would be Pythagorean Theorem; however, if they do not discover this topic, this diagnostic assessment tool will help me determine where they are at in their learning.

Works Cited:

Davies, A. (2011). Making classroom assessment work (3rd ed.). Courtenay, B.C: Connections Pub.

McTighe, J., & O’Connor, K. (2005, November). Seven Practices for Effective Learning. [Web article]. Retrieved January 21, 2017, from http://www.ascd.org/publications/educational-leadership/nov05/vol63/num03/Seven-Practices-for-Effective-Learning.aspx

Patti (pafirth). (2012, May 14). Diagnostic assessment ideas. [Slideshow]. Retrieved January 21, 2017, from http://www.slideshare.net/pafirth/diagnostic-assessment-ideas-12934737

“Blog about it” Entry #2

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Attribution

I believe that the teacher’s beliefs about mathematics highly influences their classroom environment and how the students act in the classroom setting. When a teacher shares their mathematical beliefs with their students, the students will have an idea of how the class will be taught, and what their expectations should be. For example, if I believe that mathematics is simply drill and practice, my students will expect to have many worksheets on solving similar questions over and over again, and they might have a sense that the class will be taught through the traditional approach; lecture, examples, and worksheets. However, if I believe that mathematics is something that students explore and discover, my students will expect to be given questions that require more reflecting and understanding, as opposed to a one line answer. My students would have a sense that the class will be taught through an inquiry approach, where the students discover and understand concepts using their own problem solving skills as opposed to being told what to do and how to do it. I believe mathematics is important to learn because it is everywhere in the world. People use mathematics every day, whether it be estimating what your total will be while grocery shopping, or working as an engineer and using advanced mathematics everyday. Obviously people won’t be using the quadratic formula everyday, or they might never use it at all, but people should see that mathematics is used in everyday lives. I believe mathematics is something that everyone should know and come to love because it helps you in many different ways.

  1. I believe that students should be discovering and exploring different ways to approach a question, as opposed to being given one solution path and solely following that specific path.
  2. I believe mathematics should be taught through an inquiry approach where students are expected to develop their own understandings of mathematics, but still allow time for the traditional approach to take place if need be.
  3. I believe students should be allowed to use different manipulatives when understanding mathematics, and I believe these manipulatives should be accessible at all times. These manipulatives may include connecting blocks, graphing calculators, peg boards, technology, etc.
  4. I believe mathematics is something that is used in everyday lives and should be taught in a way where students will see that they can use their mathematical knowledge outside of the classroom setting.
  5. I believe mathematics is something that everyone can come to understand if they are taught it through an approach that benefits them. This is why I believe teachers should make adaptations and accommodations for students, and should differentiate their teaching instruction when teaching a mathematics lesson.

“Blog about it” Entry #1

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Attribution

While writing my mathematics autobiography I began to reflect on my past experiences with mathematics. I have always enjoyed mathematics, however when I was transitioning from elementary school to high school, there was a time where I began to hate math. Since I was in the French Immersion Program throughout my schooling I was taught most subjects in French. Throughout elementary school I learned math in the French language. It was fairly easy for me to understand the mathematical concepts that were presented in the French language for I was never taught math in the English language in a classroom setting before. However, as I transitioned into high school, my mathematics classes began to be taught in the English language. I was so accustomed to learning mathematics in the French language, that I didn’t know what any of the vocabulary/terminology was in the English language. I remember feeling frustrated and angry whenever I was being taught mathematics because I couldn’t figure out what the words meant. After a couple weeks I began to enjoy mathematics again because I was finally able to understand the vocabulary.

While looking back on my experiences with mathematics I begin to think of things that could have helped me while transitioning from the French language to the English language. I believe that if I did more hands on problems and used more problem solving strategies, I could have been able to adapt quicker to the change. I believe if I was taught through more of an inquiry approach as opposed to the traditional approach, I would have been able to continue understanding the mathematical concepts, even if I didn’t know the specific terminology. Mathematics is something that not only needs to be taught, but needs to be taught in a way where people will want to use it in their lives and will come to love it. I hear the phrase, “I hate math”, way too much in my life, and I admit I use that phrase too from time to time; however I want to begin hearing the phrase “I love math”, and to hear that we need to begin teaching mathematics in a way where ALL students will be able to learn and understand it.