Assessment

Assessment - it's supposed to improve student learning, and yet it can often elicit anxiety or doesn't quite fulfill its purpose. How many times have you seen students skim through their assignment to find their mark, disregarding the comments, or have you yourself done this? Last year a student at my placement threw his rubric right into the garbage after reading his grade... not the response you'd hope for.

In my experience, I benefited greatly from teacher conferences or meetings where the teacher and I reviewed an assignment together or talked about strategies to improve and grow as a learner. Having  a conversation with the instructor and then developing a goal and strategy to meet that goal helped me to visualize the next steps in my learning.

One year my class had a teacher return our assignments with grades and comments and the chance to resubmit them with corrections. I was so used to the finality of a letter or number grade with no chance for redemption that I jumped at the chance to do better. Who doesn't want an opportunity to improve?

Dr. Gregory Firn developed six characteristics that align well with the models we have been given for assessment in the Math classroom:

1. Develop a meaningful feedback loop. Effective Math formative assessment provides on-going data that changes what both the teacher and the learner are doing.
2. Real-time feedback. Timely feedback—while students are learning—is critical so that students don’t practice new math skills, again and again, in the wrong way.
3. Independent learning. Ideally, blended learning is employed so that students are able to engage in some informative assessing activities independent of the teacher. This is how students learn self-assessment and gain confidence.
4. Personalized learning. Personalized learning and individualized instruction are now recognized as crucial elements of student-centric teaching that fosters real progress and achievement. This is a significant departure from the way classrooms have been structured in the past as a “one-size-fits-all” environment with all students generally receiving information at the same time and same way as their peers, regardless of their prior knowledge or academic strengths and weaknesses.
5. Active learning. As Cathy Fosnot emphasized in her webinar, Dynamic vs. Static Assessment: A Growth Mindset Perspective, “Assessment should inform lessons and learning dynamically and formatively, not statically… It captures genuine mathematizing—learner strategies, their ways of modeling problems, and their understanding of key mathematical ideas. Bottom line, assessment needs to be continuous, dynamic, and adaptive so that it can capture where the child is on the landscape of learning—where they have been, what their struggles are, and where they are going next
6. Collaborative implementation. A team effort, involving educational leaders at all levels across the school district, is required for successful implementation of a culture that supports an effective assessment culture. This effort includes sufficient resources (human resources, materials, and funding), ongoing teacher professional growth, and community engagement in developing the vision and plans for implementation.

I'm curious to see how assessment will change over the course of our teaching careers. I definitely would love to see us move away from grades but I realize that may be a long time coming or not at all. 

Why high-flying Singapore wants more than grades

Blended Learning

I love integrating technology into the classroom instruction and activities. During my placement last year I was fortunate to have access to a smartboard every day in the music classroom. I loved incorporating Smart technology into my lesson plans and the students' activities but I don't think I truly managed to create blended learning opportunities.

I think most of us aspire to be the teacher that uses technology to enhance our students' learning, but moving beyond technology integration into the blended learning world is intimidating and will require a lot of learning on our parts. The biggest take-away for me this week was the pedagogy wheel. This was the first time I had read about the SAMR model and this infographic lays out the various level of technology integration beautifully! I especially love that it suggests potential apps for different goals.

Retrieved from https://designingoutcomes.com/assets/PadWheelV4/PadWheel_Poster_V4.pdf

In our language arts classrooms we are currently developing a learning object in order to flip the classroom and allow students to fascilitate their own education collaboratively. This is what we want in our Math classrooms too! As much as I am continuing to grow in my confidence with both doing and teaching Math, I still struggle to find the right resources to achieve a truly modern and exciting Math lesson. How often do you head over to google for some lesson plan exemplars or ideas to find the Math of your past!! Quizzes, tests, independent word problems...

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If just looking at those Math ideas makes me anxious and well... makes me gag... then surely I can't put students through the same misery.

Finally, if we how valuable it is for students to collaborate we must realize how important it is for us as teachers to do the same! I have included a link from Pat's slides this week that includes suggested apps to fascilitate excellent Math teaching! Perhaps we can begin developinig our own Math learning objects in the future or atleast begin to explore the SAMR model and strive to create a blended Math classroom. 

Best Websites for Teaching

I read some simple starting steps for creating a blended learning experience in your Math classroom that are worth sharing

• Find ways to make Blended Learning fit your teaching style … unless you want to completely overhaul your methodology. In which case, I say jump in with both feet and go for it!
• In the beginning, stay close to your digital tool comfort zone.
• Not all ideas will work the first time, but try it a few times before moving on to a new idea.
• Adopt the motto: start small … grow big!
• Most importantly, be persistent. If you hit a wall, crawl out through a window and start again!

If I were a Rich Task... Daidle deedle daidle Daidle daidle deedle daidle dum!

So, I have to start my blog today with a little shout out to Trish. Trish made an excellent point today which modeled an excellent attitude for planning and creating rich tasks. She said that although she may take a really long time to develop them now, she knows she will improve and become more efficient overtime so teacher's should be brave and implement them even if they're intimidated at the prospect. I could hear Ms. Frizzle's voice in my head... "take chances, make mistakes, and get messy!!!" We should not be hard on ourselves just because this part of Math planning is difficult! We are still learning and we would be cheating our students if we don't take the time to develop these skills as Math teachers! So, thank you Trish for encouraging me to be brave and keep on keeping on...

In the article "Rich Tasks and Contexts," Jenny Piggott provided an excellent list of the components of a rich task:

• are accessible to a wide range of learners,
• might be set in contexts which draw the learner into the mathematics either because the starting point is intriguing or the mathematics that emerges is intriguing,
• are accessible and offer opportunities for initial success, challenging the learners to think for themselves,
• offer different levels of challenge, but at whatever the learner's level there is a real challenge involved and thus there is also the potential to extend those who need and demand more (low threshold - high ceiling tasks),
• allow for learners to pose their own problems,
• allow for different methods and different responses (different starting points, different middles and different ends),
• offer opportunities to identify elegant or efficient solutions,
• have the potential to broaden students' skills and/or deepen and broaden mathematical content knowledge,
• encourage creativity and imaginative application of knowledge.
• have the potential for revealing patterns or lead to generalisations or unexpected results,
• have the potential to reveal underlying principles or make connections between areas of mathematics,
• encourage collaboration and discussion,
• encourage learners to develop confidence and independence as well as to become critical thinkers.

This list may look intimidating at first, but remember... we don't need to include ALL of these considerations in every task.

Which one doesn't belong? 

As we delve through this Math course, I'm definitely doing my best to compile as many strategies and resources as possible to ensure as rich of a Math class experience as possible. I had never played "which one doesn't belong" but I have to say, totally love it! What a great mind's on activity that can be applied in a variety of subject! My favourite part about this activity is that it encourages students to think creatively, reason their answers, and they can all have a chance at being right! It's a great confidence booster for students and can be a great diagnostic tool for us teachers to assess vocabulary among other things. 

On my quest for resources, I stumbled across the Ontario Association for Mathematics Education! There is a hefty registration fee ($299) but the website has some interesting articles and links to free resource. I enjoyed this article on developing rich assessment tasks: Using Rich Assessment Tasks

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The modules from this week have only reinforced what I already knew about the value of collaboration. If I can clearly see the benefits that collaboration have had on me in the Math classroom as a fairly reluctant learner, why wouldn't I extend the same courtesy to my students that I can empathize with? Not only do I get the chance to process my thoughts out loud (which is very important for an external processor) but I can also maneuver through the mathematical processes with confidence because I have so many great minds by my side to offer insight and strategies that will embed my learning!  

Out with the old mindset, in with the new!

I'm not going to lie. I found class this week to be rather challenging. When I see Math word problems I immediately feel resistance and trepidation about tackling them. There are other branches of Math that I can totally engage in right away without fear of failure...(although why the heck I fear failure so much is beyond me...)  but the format of the questions we were looking at this week were not up my alley.... yet ;)

Thankfully, I noticed a small printed sign on the ledge beside the smart board yesterday which encouraged me to hit the reset button on my attitude.

TidyLadyPrintables. (2017, August). Mistakes Are Proof You're Trying [Image]. Retrieved September 19, 2017, from https://www.etsy.com/au/listing/491102736/classroom-decor-mistakes-are-proof-youre

What an excellent reminder for students and adults alike! Mistakes aren't the end point or a sign to give up, they are simply part of the process which we can overcome! And as we have learned in this week's modules, they help our brain grow!

I definitely admire people that continually display a healthy attitude about mistakes and who model a growth mindset. My husband and I are fans of MasterChef Australia and our favourite contestants on the show are always the ones that have the best attitudes and who work extremely hard. They are excellent models of what true success looks like, not admitting defeat, working hard with a smile and overcoming adversity. I think it would be great for students to choose a growth mindset hero that they look up to and can model their behaviour after in the Math classroom!

This week we developed some great strategies for getting started that we can implement with our students. My favourite strategy was including parallel tasks in a lesson plan as it provides students with choice! I was relieved to see that I wasn't stuck with just one tricky word problem to choose from, instead I got to choose a word problem that would challenge me but not discourage me from moving forward.

The biggest obstacle I can see in teaching Math is helping students get started on Math tasks. I really enjoyed the opportunity for us to collaborate in small groups to formulate common and scaffolded questions that will help us to plan ahead for what our students may ask us but also to help students develop strategies to get started on their Math tasks and persevere through challenges. My next step will be to start accumulating resources to help me grow in understanding for how to develop parallel tasks and
good questions that will help students develop confidence in their problem solving abilities.

I have included a link to an edugains video that is focused on effective questioning that may be a useful resource. 

Edugains. Learning Through Effective Questioning [Image]. Retrieved September 19, 2017, from http://www.edugains.ca/resources/ProfessionalLearning/SelfDirectedPLM/DigitalPapers/effectiveQuestioning/planPowerfulQuestions.html#

Plan Powerful Questions

Knowing/Doing vs Understanding

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How many of us have negative lurking beliefs about ourselves from our childhood that still impact us today? This has definitely come up in our Math class this and last year as many of our fellow teacher candidates are self-professed Non-Math people.

The modules this week challenged me to assess whether I've been reverting to a fixed mindset about Math. They also defended the research that shows how beneficial a growth mindset can be to an individual's success. Aaaaand huzzah for neuroplasticity!!! The brain is so flexible and our intelligence isn't in a fixed state. I'm so glad the research supports what so many people have been saying for ever! That practice pays off, you can get better and if you work hard you are unstoppable! Now to transfer that attitude to students and help them on the road to success.

This week in class we discussed the importance of knowing/doing Math vs. understanding Math. I grew up with a rote heavy learning style. I studied Music (scales for hours, and hours, and hours), French, Latin & German (oh sure, I'll conjugate a million things again... and how about some more flashcards?) and Math ... oh the multiplication drills. Yikes.

A Little Princess. [Pinikir Fox]. (2016, November 7). A Little Princess 1995 Classroom Scene [Video File]. Retrieved from https://www.youtube.com/watch?v=FjWm8dm-k08

I do know that there is value in practicing, drilling and repeating exercises. However, I could not make connections or explain why something worked in Math class and was left to guess or make up an answer if I didn't understand a problem.

This is why the "How Old is the Shepherd?" video resonated with me so strongly. I understand why students would simply guess or try to rationalize why they should have an answer and try to solve the problem instead of saying that it wasn't possible. I have definitely witnessed students use funky strategies in the past that were not needed or not relevant to a question before because they didn't know how to break down the question so it made sense to them.

I really liked what Pat said about challenging students with questions that are difficult and they will probably be unsuccessful with at first because as they learn new strategies and work towards getting the right answers their Brain actually changes and grows! But we still need to give them strategies to really understand how to solve a math problem.  The daily three activity we did as a class helped us think of way to tailor a lesson plan that is inquiry based and collaborative!

I really love new challenges. I'm definitely the type of person who loves to fight complacency and take up a new hobby or activity to continue to grow and change as an individual. I have personally experienced a change in my attitude toward teaching Math and I know have greater self-efficacy about potentially teaching it in the future. Maybe in November even! I just need to continue to have a growth mindset about teaching this subject. It's so easy to be complacent and revert to old strategies that we have found successful in the past instead of embracing new methods of teaching and embracing the unknown while facing all the fear that may come along with it.Now to share with my students the personal successes that I have experienced because I kept trying... not just because I was a natural or "smart."

Aaaaaaand We're Back!!

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Oh there's that familiar feeling. My brain is finally rousing from its summer slumber to the cold, harsh reality that is Math Class.... Okay, maybe I'm being dramatic. We got this! Thank you Kelley for reminding me to have a growth mindset. Bonus marks for you ;)

Firstly, how great was the game about squares? I'm not going to lie, this got me pretty pumped about getting back into Math.... but did I really leave? Hmmmm (math is everywhere).

 I love puzzle games (portal anyone?) and a little competition never hurt anyone. This is a great way to engage students that thrive in competitive situations to challenge themselves to think outside the box. There is a challenge that presents itself however when you want to get the class to transition to another task. I admit that I initially had a hard time getting focused on the next task.

Game About Squares. Level 24 [photo]. Retrieved from gameaboutsquares.com

After we had solved a few puzzles we consolidated as a class to discuss the different methods we had used to problem solve and it was really interesting to hear the different approaches that classmates used in order to be successful. Just goes to show how important it is to diversify your instruction to meet your different learners. Not only that, but it also shows how much the class can be involved in its own learning! Students can work together and learn from each other, teachers must remember to facilitate learning among peer groups.

I really enjoyed watching the video in which the speaker had suggested to a curious little child that kept looking to their father to explain what something was to them, to ask themselves what they thought about something. This is a wonderful way for children to become more autonomous in their learning and empowers them to figure something out, instead of just looking for the "right answer" from their teacher. This also communicates to students that they have something to offer to their peers and they can find it within themselves to think creatively and uniquely about a Math problem.

I remember from last year that I really appreciated more open Math questions as they do not simply ask students to find a formula to solve a question.

Overall, the most important thing to remember is to ensure that real life application comes into play as much as possible. So many of us don't even realize how often we are using skills we learned from Math class, this can occur multiple times a day! By providing students' with a context in which they can use their Math skills in real life it gives them a chance to practice it and also to appreciate it.

Data Management and Probability

Class Dojo

I loved the little class dojo video that we watched this week to kick off our class! A growth mindset is something I myself am still working to attain. I have made sure to be careful of the language I use when I am frustrated even in this class whenever I come to a difficult point in a problem or feel like I won't ever find the solution. I want to make sure I model an attitude reflective of the growth mindset when I speak to students about any subject. Recently, this has been important when teaching grade six students as they start on their instruments for the first time. It is a very steep learning curve and many students get intimidated or frustrated quite quickly. This is why you must be sure to encourage and celebrate persistence!

Data Management was my BIGGEST worry for this course. That was the very last math class I took in highschool and it sealed my fate when I decided to never again take a math course... or so I thought. 

One of the first activities we did in class this week was to guess how many Oreos were in a big clear container. I have played this game many a time at baby showers or wedding showers and I have never, ever won. My mother however, the spatial guru that she is, always wins! This time I actually got fairly close to the answer, so I was proud of that... Maybe now I have a chance of getting it!

If only Data Management and Probability had been taught with such soft language when I was a youngin! Maybe then I wouldn't have been so overwhelmed with questions and frustration as I struggled to apply the instrumental algorithms we had thrust upon us. 

We went around the class and came up with examples where we had to estimate things in our daily lives. I thought this was a great way to avoid the question - "but how does this apply to real life?" Of course it does! We estimate things all the time! Data Management is simply the process of doing something with the DATA that you have collected! 

Do kids still get things from cereal boxes?? I remember getting some pretty great prizes when we were little. One of my favorite prizes was a nintendo game, we had to save up 10 cereal box tabs and mail them away and we received the Mario All Stars games. In this case, we were trying to determine the odds for receiving all six prizes using a dice (or number cube). I was really surprised by the variety of responses throughout the room! Harpreet and I managed to get all six in only seven rolls, but our second attempt took us 31 tries! That was really interesting to explore through the Tinkerplots. The more attempts you have, the more you really get to understand the overall chance or probability of something occurring.