Assessment

This week we covered assessment. Something I found interesting was what the curriculum teaches us about assigning grade levels. For instance, how many of you knew that by meeting the curriculum expectations, a student would receive a level 3? Prior to teachers college, I always thought if you met all of the expectations, you would receive a level 4. However, what we have learned is that you can only assign a level 4 if the student goes above and beyond the expectations.

Ministry of Education. (2005). The Ontario Curriculum Grades 1-8 Mathematics. Retrieved from: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Another interesting point was the research that was discussed surrounding grades and comments. How many of you can admit that you are concerned about the grade when you submit a piece of work? I know this is something I personally care a lot about. The first thing I look for is the grade I received, followed by comments on how I can get a better grade on the next assignment. However, research has proven that if a teacher reveals a grade to a student, they have a zero percent likelihood of improving on their next assignment or test. In contrast, when teachers left comments on the student’s work, with no grade anywhere to be found, students were at a 30 percent more likelihood of improving the next time. This increase in likelihood of achieving higher results is a significant amount. What does this show us then? How should we mark students work? Well, what the research has shown is we should be recording marks for our eyes only, and only letting students have access to the comment portion of the marking component. To compare, the research has shown that if the teacher records a mark alongside the comment, the student returns to a zero percent likelihood of achieving higher results next time. This is because students place more emphasis and care on the grade, as opposed to the feedback that they are being given.

Kevin Hodgson. (October 11, 2015). Hit with the growth mindset. Retrieved from: https://www.flickr.com/photos/dogtrax/22075424832

Knowing this now, what are some strategies we can use when leaving feedback for students? Well, students respond well to compliments, though we cannot leave it at just a compliment, as this will encourage a fixed mindset, which is to be avoided. Instead, provide your student with a compliment about a strength you see in their work, a “wonder” component where you question something about the work, and a challenge you saw. This way, the student leaves the comment with a growth mindset, and they can leave with useful advice on how they can improve for next time.

We took part in an activity in today’s class that demonstrated our ability to leave descriptive feedback on student work. We were encouraged to find at least two ways that a student might solve the problem. After solving the two EQAO questions each, we had to work together in our table groups to look at how a student solved these questions. Whether the student got the question right or wrong, we had to dissect their work to see what their strengths and challenges were, as well as an “I wonder” component.

The image above shows how I answered the two questions that were assigned, whereas the bottom image shows how Ross and I dissected the student’s answer and provided feedback for their work.

Overall, the main points to take away are these:

1.       Always leave a strength, “wonder” and challenge when leaving descriptive feedback;

2.       Make sure your feedback demonstrates a growth mindset;

3.       Leave comments on student’s work as opposed to grades/comments and grades as this will result in a higher rate of improvement;

4.       Level 4 is for the students that go above and beyond the expectations.

Blended Teaching

Blended learning is a way of incorporating digital and web tools into your teaching instruction and student activities to enhance student learning, which also allows for students to work at their own pace.

The document you will see below entitled “The Basics of Blended Instruction” discusses some tips for blended instruction. Out of the five tips that Tucker shares, I found that the one I most related to (at least from my experience in placement) is tip #3 “technology shouldn’t be just a frill.” Technology can replace the traditional lecture style teaching, and/or also allows for further and more engaging ways of teaching content to your students.

For more information on Blended Learning, and to see which tip you think best relates to your teaching style and your classroom situation, please visit:

The Basics of Blended Instruction

Blended Learning Models

https://www.youtube.com/watch?v=QF8ODHN6Os8&feature=youtu.be

During station 3 for our blending teaching learning session, we watched a video which broke blended learning into 4 models. Below are the names of each model and a brief description from the video.

Model	Description
Rotation Model	Includes 4 submodules, which are station, lab, flipped and individual.
Flex Model	Online learning is the backbone of student learning that allows students to move at an individual pace.
A La Carte Model	Taking one or more courses entirely online.
Enriched Virtual Model	Students divide their time in a school setting and online. Most began online but ended up turning into blended learning.

SAMR Model

https://www.commonsensemedia.org/videos/introduction-to-the-samr-model

During station 4, we moved on to the SAMR model. We learned that the substitution and augmentation levels are for enhancement of learning, whereas the modification and redefinition stages are for transformation of learning. Below is the chart that I filled out during this station, with information and examples from the video watched.

Level and brief description	Give an example of each level
Substitution – tech acts as a direct tool substitute, with no functional change.	Creative writing using the word processing program.
Augmentation – tech acts as a direct tool substitute, with functional improvement.	Creative writing using spellcheck and formatting.
Modification – tech allows for significant task redesign.	Creative writing using google docs to get real time feedback.
Redefinition – tech allows for the creation of new tasks, previously inconceivable.	Transform stories into a media video.

Padagogy Wheel

http://designingoutcomes.com/assets/PadWheelV4/PadWheel_Poster_V4.pdf

When I broke down the criteria for the padagogy wheel into the achievement chart categories, this is something I came up with for how you can assess the students through the various stages:

Knowledge/Understanding: remembering criteria and understanding criteria.

Thinking: Analyzing criteria and evaluating criteria.

Communication: Applying criteria.

Application: Creating criteria.

Allan Carrington. (March 13, 2013). "The Pedagogy Wheel". Retrieved from: https://www.flickr.com/photos/allanadl/8553210313/in/photolist-e2Prrk-51YEnw/

Tellagamis

At the end of the blended teaching activity, we had an assessment question. “You and your group will use an iPad to create two 30 second animated Tellagamis. One will summarize Blended Learning, and the other will briefly explain the SAMR model,” (Blended Learning Worksheet).

This is a great example on how you can incorporate technology into your student’s learning. Let your students work through a series of task to better understand a topic, with the help of the Internet and technology. Then, you can have your students explain their findings by using an app like Tellagami to share their findings. This is one way to keep your students engaged after working through a series of stations at their seats, and a great way to wrap up after working on a worksheet. You could have your students hook up the iPads to an HDMI cord and play their Tellagamis in front of their classmates as a reflection and/or sharing consolidation.

Keeping your Students Engaged through Rich Tasks

Want to keep your students engaged? One way to keep them engaged all year round is through mutual celebrations. Kids like when you celebrate everything because it shows them that what is important to them is also important to you. We should encourage our students to share, so that we can all celebrate with them, in order to show them that it is something important and worth celebrating to everyone. I wonder, did any of you celebrate with your students during your placement? What types of things did you celebrate? I know at my placement, we celebrated the students birthdays by having the students sit in the teacher’s chair at the front of the classroom, while everyone in the classroom sang them happy birthday

What are some other ways to keep students engaged in the classroom though? How can we keep students engaged in mathematics, knowing that not all students may enjoy math?

Dan Meyer Talk at Cambridge NRICH/PRIMAS day

Kids like when you include your real life into the math problems. When discussing the ski jump and slope, Patricia included her personal story about skiing, with herself and her family. Therefore, even though she was discussing a good resource to refer to (Dan Myers videos), she was able to include her own personal life into the problem to keep students interested, as some of us who took the class with her last year had already known about the video reference. Side note, Patricia not only included her own personal life in the example, she also included her previous class from the year before by bringing our class into the example. This helps to keep students engaged because it allows them to jog their memory to recall the example provided last year, that we are now referring to again this year.

Another way to keep your students engaged is through rich tasks activities. We participated in multiple rich tasks activities this week, though this one was our minds on activity. The activity involved solving a problem that suggested a classroom of 24 students during lunchtime. Half of the students play soccer, a quarter of the students play on the adventure playground, a sixth of the students sit around and the remainder play tag. Then you are asked to add the teacher to the group that sits around during lunchtime. This is how my table group solved it:

Tips to consider when introducing rich tasks into our classroom:

• Opportunities for extension – kids might like the problem they are working on, so you can keep them engaged by extending the problem when needed.
• Give students time to complete the tasks so that everyone is able to try to solve the problem, rather than getting the answer from someone else. There may be students who need to finish the problem and could get upset or flustered if they are not given the time to complete the question.
• These tasks need to be in the middle of your lesson to allow students the time to complete them.
• Students can learn from each other because they are working together. They may start the problem differently, which again, can allow for students to learn from others. We see this in the Math Mindset Module this week too with the question 18x5. We all had our own way of solving it, some solving it the same way others did, while others solved it in a way that we may not have ever thought to solve the equation. Whether through the video or our fellow teacher candidates’ forum posts, I’m sure that we can all agree that we learned something from this problem.

I leave you with this question, one that has come up in class this week. What makes a rich task? You may wish to refer to my blog from last week if you would like to collect resources for rich tasks for mathematics.

Parallel Tasks - Offering Options for Your Students

Remember that game we played at the beginning of class on Monday? Where you were given a number and you had to say “I am (number), who is (problem)”? This game is used to encourage students to think and participate in math class. Calculators are not permitted to be used during this game. Furthermore, you may recall that we played the same game in last year’s math class except we used different questions.

Parallel tasks gives choices which will have your students want to participate. Reading both questions may help the student to better understand the problems. They are also beneficial because it provides your students with a productive task to complete, while encouraging critical thinking. In addition, parallel tasks allow your students to work at their level.

 If students choose a challenging question, let them. There is a good chance they may go back and choose another question. But if a student chooses a question that is too easy, have them come up with multiple answers or assign them a second question. This relates to our online math mindset module this week, where we learn about math and speed. We want to encourage deeper thinking, so give your students a challenge to help develop brain growth.

In addition, one way to encourage deeper thinking is by providing parallel tasks in a group setting. We witnessed this in this week’s class, where we were put into groups, and given a number of parallel tasks to choose from. Once completing the tasks, we were to participate in a gallery walk, making suggestions on other group’s work and/or mentioning things that we liked about what they came up with. This is something we have done in other classes such as Social Studies in year 1, though I never experienced this during placement. I would definitely like to take more initiative in placement and ask my associate if they would be willing to allow for the class to participate in an activity like this one. The question that my group decided upon, out of all the questions Patricia provided us was:

Choose one of the measurements below. About how many years old is something that is as old as the measurement you chose?

-          1000 days

-          10 000 hours

-          1 000 000 seconds

Below is a picture of the chart that my group came up with.

Another parallel task was the question we answered about jeans. This is the question I chose to answer: “Jamie paid 80% as much as Juliana for her jeans. If Juliana paid less than $50, how much might each have paid?” Below is how I solved the question. How did you solve it?

Since I am someone who enjoys shopping, the first thing that came to mind was adding tax to the pair of jeans. I would not expect the same from my student’s, though I would be highly impressed if anyone in the junior or intermediate level thought to do that.

On a side note kids like when you include them in problem. You can do this simply by having their names within the questions. Did you notice how Patricia included my name in addition to another student teacher’s name in the math problem? This was also done within the parallel tasks group table questions too!

Additional Resources

Next week we will be discussing rich tasks. If you would like to get a jump start on looking into some rich tasks resources for mathematics, feel free to visit the following websites that I was provided with during my first teaching placement:

 

Released EQAO Questions

NRICH: Enriching Mathematics

 

Yummy Math

 Mathalicious

 

 

Making Math Make Sense

This week we discussed an important question. We were asked if it is more important to know/do math, or to understand it. As much as we want our students to do math, as it is required, it is more important that our students understand what they are doing. Often times, students will memorize information, and only retain it for as long as they need it, like a test for instance. However, this is not what we should strive for. It is much more beneficial for students to understand what they are doing, in order to retain in within their long-term memory, which will allow students to come back to their learning at any point in the future. How do we go about doing this though? How do we truly get our students to understand math? Simply put, we have them practice, practice, practice.

As educators, we need to differentiate the instruction in all subjects. One way to do this is through visual aids. Regardless of what a student’s learning style is, visual aids can be beneficial to all students in math class. If you are working through a math problem, odds are it will be quicker and easier to solve if you have the problem right in front of you to work with. For instance, when we were asked to count to 1000 on our fingers starting at the thumb, on one hand, we had to conclude what finger we would finish on. Rather than students counting to 1000, there are ways you could come up with to speed up the process. For instance, I drew my hand on a sheet of paper. I noticed that my pointer finger and my ring finger were always even numbers. Therefore, every time I went up another 10, I wrote that number above the finger it landed on. Once I got to 20, I kept jumping back and forth between the two fingers until I got to 100. When I found out what finger 100 landed on, I knew that would be the same finger that 1000 landed on. As a result, 1000 fell on my ring finger. This is a visual of what it would look like:

 Einar Jorgen Haraldseid. (October 4, 2006). My hand. Retrieved from: https://www.flickr.com/photos/ejh/260959129/in/photolist-p4u4k-fZL6AG-fn8ZQK-DkL-hu399v-2gmPu-cftf7w-dcxmXb-99sLpa-4ji5Lv-5uh8Jv-aRzMCi-2T6KoD-eWKQtL-HmGB7-NoNmb-bqWDkG-84WcqY-oPgLGj-prRbCC-hu1MSi-hu1Pmk-5XRxkZ-8QyBGF-an69JF-djYDXd-34WfVK-62w2QS-5XRHPr-cvUW9h-ciHSTy-bcsP8X-hu1PKM-rnpSoc-d7hvry-5XW1e3-e1GnbW-ehTDCD-5wjKQt-34km4-eWgczG-5uh41F-2gny7-eW3yMX-4CdoFR-98ALqu-9VV5yq-5XS6bF-5XSgyn-4AcQZm

Lastly, an important thing to remember is that when asking any question, it has to make sense. For instance, one of the questions that students were asked was about a shepherd having 125 sheep and 5 dogs in a flock, how old is the shepherd? As educators, we know this question does not make sense because there is no way a student can find out the shepherd’s age based on this question. One proper way to word this question could be:

At 20 years old, a shepherd inherits 25 sheep and 1 dog for his flock. Every 2 years, the shepherd adds 25 more sheep and 1 more dog to the flock. How old will the shepherd be when his flock has 125 sheep and 5 dogs?

This question makes much more sense because it gives students enough information to do the math to solve the problem. This is just an example that demonstrates how a math problem must make sense so that students can solve it. I give credit to the students that still attempted to solve the problem because you could see where their thought process was.

To summarize, I would hope that you take three things from this post:

1.      Make sure your students UNDERSTAND the math

2.      Visual aids in mathematics are beneficial for ALL students, regardless of their learning style

3.  If you ask student to solve a math question, make sure the question makes sense! 

Thanks for reading!

Hello and Welcome!

Hi there!

This blog will serve as a continuation to my former mathematic blog postings. For my fellow teacher candidates, welcome to year two! I hope that there may be information that will be useful to you as we continue our final year of teacher’s college. I hope to share more personal experiences this time around, as I now have completed my first of three teaching placements. Let’s begin!

This week has been busy for math to say the least. With having the holiday Monday, we lost a day this week, which has been overwhelming when it comes to doing the online portion of the course. However, as overwhelming as it was to hear what was all due, it was a lot less overwhelming actually completing the tasks. Good news right?

There are a couple things I want to talk about in this blog in regards to what I have learned so far from our first class and the online module. This week I learned something when taking part in the “Game about Squares” online game. While playing the game, the first few levels were a breeze to get through. By the time I reached level 12, I started to really struggle.

I became frustrated because no matter how many times I tried to beat that level, I just was not getting it. Was it that I don’t like to make mistakes? Well, let’s be honest. Not many people would say they like to make mistakes. However, I am okay with making mistakes; it was the fact that no matter how many times I attempted it, I felt like I was getting no further. I decided that I would try again during my break between my two classes. Eventually, I was able to get past the level, and was actually able to get all the way up to level 22, which I failed several times before having to head to my next class.

Now that I have completed the online module, which included videos to watch, I realized something about this activity. It doesn’t matter how many mistakes I made along the way because eventually I got further with the practice. This is something that many of the videos touched upon. It does not matter how many struggles or mistakes we make because this is where we learn. Our mistakes are what enable our brains to grow, which allows us to become better at whatever it is we have been practicing. However, before watching the videos, I was sitting at my seat in that frustrated state of mind because I could not do what the game was expecting of me. This is a feeling that many students struggle with daily.

Sweet Dreamz Design. (February 18, 2014). Picasso Goals. Retrieved from: https://www.flickr.com/photos/creativegem_designs/12623792625/

It is important to remember that students are constantly learning, constantly struggling, constantly learning from their mistakes. Essentially, we are all learners, and we learn from those mistakes. Luckily, I was fortunate enough to be seated next to a fellow teacher candidate who helped me to succeed when I was getting frustrated with myself and this square game. That is our role as future educators though. It is our job to encourage students to work through their mistakes, in order for them to improve.

Math is a constant struggle for some students, if not many. There are some stereotypes and myths that many of us have probably come across during our educational years, though they still exist today and this is a problem. Some of these myths include that there are “math people”, or math, like science, is a boy subject area, which leads to the myth that girls are not as good at math as boys. The fact of the matter is, math is a subject that anyone is capable of learning and doing well in, it just takes more practice for some people over others. Rather than participating in these myths and stereotypes, we should encourage students and even adults, to develop a growth mindset. This mindset demonstrates how you can learn anything as long as you spend the time practicing whatever it may be. Personally, during my placement I wanted to challenge myself after learning about this growth mindset. I knew that math was a challenging subject for some students, and therefore, I wanted to change the mindset for the students who had a fixed mindset in regards to their ability to do well in math. Although I did not have a long period of time with these students, I could see their mindsets changing little by little, as they improved on their prior mathematical skills. It was rewarding for the student and myself, to see them changing their attitude towards their own capabilities in math.

If you want to try out “Games about Squares,” please visit the following link:

Game about Squares

 Thanks for stopping by!

PS - on a side note, when looking for images, I came across a blog that some of you may find useful! If you are interested in viewing it for resources or insight, please click on the following link:

Jill Dawson Blog

Final Reflection Week 12

 

Final Reflection

We have now come to an end in our first year mathematics course. I must say, I feel like I have come a far way since the first class back in September. I remember entering day one, and we were instructed to write on the Smartboard one word that describes the way we feel towards math. The word I chose was “challenging”. I started becoming really comfortable with mathematics in grades 11 and 12, though I did not major or minor in the subject for my undergraduate degree. Therefore, I was rather nervous entering the course, not remembering formulas and terms. However, it did not take long to get more comfortable with math again. Although there are still some challenges I face in the activities, like the one during week 11 “co-operative group activities,” where we went around in groups of 3 to solve problems at different stations (such as number charts, blocks and stick figure stations).

In addition, I enjoyed the digital word problems that we had to create. It was a fun way to think about math in your everyday life. I really enjoyed looking at my classmates’ word problems, as I found 3 right away that I could relate to. I was happy to see that Shannon had found my math problem relatable as she had commented saying she had just finished painting her basement. It was nice to see that not only could I relate to what my classmates posted, but that there was at least one classmate who could relate to my world problem. Also, although we were instructed that you couldn’t create a word problem on something that has already been done, I found that everyone was very creative and had a wide range of math topics covered. I was really impressed with what the ones I read had come up with for their problems.

Overall, I am very pleased with this course. Leaving this course, I am not afraid in terms of my capability to teach mathematics. Also, I look forward to the class next year, although the setup will be different as it is said to be six weeks rather than twelve. I wish that we could all be in the same class again next year, to see how we have all grown after we teach math in the New Year. It would be interesting to see how comfortable the entire class felt towards it, and how they feel about math after teaching it. Furthermore, I felt that although we were a fairly quiet bunch in terms of classroom discussion aloud, we were given the instruction needed in order to become more comfortable in this subject before our teaching block begins. The Great Games definitely helped along the way because rather than just reading out of the textbook (which was also very helpful and I will never get rid of that textbook), the games helped to make sure I knew what I was doing for that particular unit of math that we were studying that week.