Now for people that know me, they’ll realize that most of my tweets are for things I’m truly grateful for, and a few, are not. Why am I doing this? It’s not in an effort to be deceitful. If people asked, I would be honest. It’s because I’m trying to test the power of positive thinking.
If there’s something that I’m less excited about, something that bothers me a bit, or something that makes me upset, and I tweet about it in a positive light, am I more likely to approach the situation in that way? Am I more likely to end the experience in a happier mood because I started in one?I’m thinking that the answers to both of these questions are “yes!”
Last week, two of my #gratitude tweets were not as genuine as the rest, but approaching both situations with a smile on my face had me leaving with one too. Did things go perfectly? Not exactly — but some #gratitude led to a happy day!
How does your attitude change your outlook on a situation? I’m curious how others may be testing the power of positivity!
Aviva 🙂 Determined to start and end my day with a smile!
This year, I decided to join an educational Book Club hosted by our Board. We’re reading and discussing Stuart Shanker‘s book, Calm, Alert, and Learning. Now this was an interesting Book Club, as it was advertised through our Board’s KinderConference but open to anybody. I’m very interested in the topic of self-regulation, so I thought that I’d register.
We met for the first time last week, and I quickly realized that I was one of the few people not working in a Kindergarten classroom. I started to wonder a little bit if I made the right choice to join the Book Club. Today, I decided that I did.
I just read the second chapter in Shanker’s book on “The Emotional Domain.” Wow! There are so many important points in here that need to be considered for all grades:
How do we not just see “emotions” in a negative way?
How do we regulate our own emotions, as teachers, so that we can calmly support our students?
How can we use a gradual release of responsibility model — in all grades — to help students take more control over their own emotions? What does this model look like in the different grades?
How do we address the varied needs of our students? I can’t help but think back to the 1+1+1 blog post that I wrote on the 19th.
How do we remember the impact that culture can have on emotions? How do we address this in a classroom context? I think here about Aaron Puley and his constant reminders about seeing things through an equity lens. This is so important here!
What impact does differentiated instruction have on this emotional domain? How can we make our learning environment — regardless of grade — more about “student voice” and “student choice?” I definitely see the connection between the ideas discussed in Shanker’s book and our current school focus.
As a teacher that’s now had experience teaching every grade between JK and Grade 6, Shanker’s book reminds me of the overlap between these grades. He makes me consider how skills that are often addressed explicitly in the early primary grades are sometimes forgotten in the junior ones (and please note here that this is my thinking about what he’s written, and not what’s actually stated in the text). Shanker makes me wonder how we can tie this emotional domain to curriculum expectations, and how we can focus on emotions regardless of grade.
While I hope that my questions and wonderings might be discussed during our Book Club meeting on April 7th, I’d also love to talk about them here. Please share your thoughts, questions, and wonderings. Let the “teacher inquiry” begin! 🙂
I decided to start things off yesterday by reading through the problem with the class.
My students were finalizing their plans for our year-end field trip, and working hard to ensure that their final choices met with our project requirements. Reading this problem made them very excited: they could save some money on their trip, and help ensure that the total cost for the students remained at $25 or less. While I wanted the groups to show me how they were going to solve this problem, I also wanted to hear some initial student thought, so I decided to record this podcast.
While I was very excited about the math possibilities for this problem, I didn’t even consider the real world implications. This is not just a make believe math problem. Students are helping to design a real field trip, so they’re thinking in terms of real life.
I would have never considered that nine students would pay for the trip, while one student got to go for free. As a teacher, I’m used to splitting up the costs to help accommodate for deals, but many of the students saw this as more of a lottery system, and they started talking about what was “fair” and “not fair.” While I was thinking in terms of proportional reasoning, they were thinking in terms of what was the right choice for everyone.
I didn’t even think about the fact that some students may not go on the field trip. Of course this is the case, as that always seems to happen, but this was just a make believe thinking question. I assumed that everyone would figure that all 90 students are going, but if this is real world, then their thinking is real world as well.
It was interesting when even this one group of four found out that they save the same amount of money with both types of deals.
When discussing this solution with the group, the students told me that even though they saved the same amount of money because of the cost of their tickets that $2 off would probably end up really saving them more because not everyone’s going to go on the trip, so they won’t really get nine people free. The group also mentioned to me that if their tickets cost more, then the nine free tickets would save them more money, but if they only got eight people free because of trip attendance, maybe the $2 off was still a better deal. It’s amazing how real life can make you reconsider math!
Real life also had me re-thinking math when I saw this group’s solution.
Please note that they meant “81 people pay” not “don’t pay.” They told me this during our follow-up discussion.
Since we’re not learning to multiply by decimals, I told the students that they could round, and this is exactly what they did. The problem is that both of these amounts round down. If a company is really giving us this deal, will they also allow an additional deal of paying less for each ticket from the get go? And this is where I re-think the concept of rounding when it comes to decimals and dollar amounts. If the real world math application for rounding decimals is in terms of money, and this is certainly a great example of it, will stores want people paying multiple cents less for an item if they’re rounding to the nearest dollar amount? Or if an item costs $8.35, the amount rounds to $8, but just bringing $8 to the store is not going to be enough to purchase the item. The math says to round down, but the real world application says to round up.
So as my brain continues to hurt this morning from all of this math thinking, I come to see what this focus on proportional reasoning is really all about. I think it’s about the “thinking.” I think it’s about the accountable math talk. I think it’s less about the answer, and more about the reasoning. As students worked through this proportional reasoning problem in class yesterday, I saw and heard a lot of math thinking. Was all of it correct? No, but our conversations that evolved from it allowed for some meaningful math learning — for both me and my students. And as I reflect more now, my learning continues. It’s with this in mind that I’m looking forward to Monday’s Proportional Reasoning Inservice with the hope that it gets me thinking even more, as teacher thinking leads to more student thinking and student thinking leads to increased understanding. Let the teaching/learning cycle continue!
What are your experiences with proportional reasoning and real world math problems? What advice would you offer me as I continue to work on developing “thinking skills” in math?I’d love to hear your thoughts!
This year in particular, I see teaching as a cycle: I teach, think/reflect, make changes, and try again. I’m really trying to embrace inquiry in the classroom, and I love how it’s making my students into better, more critical, thinkers, but making inquiry work is hard work. Teaching is hard work. And honestly, I wouldn’t have it any other way!
Please don’t get me wrong: I don’t think that I’m a bad teacher. I think that there are lots of good things that I do to help engage students in the learning process, and I have seen some amazing progress throughout the year. But I’m not perfect. I make mistakes (lots of them), and I try to think about these mistakes, make changes, and improve. Sometimes my second attempts work better. Sometimes it takes three, four, five, six, or 3,282 attempts (only a slight exaggeration 🙂 ) to make things work.
Do my mistakes negatively impact on students? No, I don’t think so. In fact, I think quite the opposite. I admit when I make mistakes, but I also show students how and why I’ve rethought things, and what I’m going to try next. Hopefully this process helps students see the power in perseverance and hard work, and hopefully my changes lead to better learning for all.
And it’s with this cyclical process of teaching in mind that I’ve made a change for today. As a Board, we’re focusing on proportional reasoning in math. Proportional reasoning is a big idea that blankets the different math strands, and really helps students develop thinking skills. Right now in math, we’re working on multiplication and division, and I was very excited yesterday when I thought of an extension for our real world math problem that connects to proportional reasoning. This is where I made a mistake though (or maybe even a couple of mistakes).
I didn’t finesse my wording before asking a group of students the question. Tweaking the wording during the discussion, I think resulted in some confusion about how to address the problem.
I didn’t give students enough “thinking time.” I have a student teacher right now, and we’ve spoken many times about the benefits of “wait time.” I’m getting so much better at this myself, but not yesterday. I think that I had a solution in my head, and when students weren’t getting to the answer in the same way (despite actually getting the answer itself), I started redirecting them too early. I didn’t ask for them to clarify their thinking. I didn’t give them enough time to explain. I interrupted and started guiding.
I was so excited to record the group discussion for the problem, but after listening to it last night, I’m reluctant to even share it here. So now what? I thought about what I did wrong, and what I would do differently the next time. Then I came into class this morning and wrote this math problem.
Today, I’m going to get groups to think about the problem together. I’m going to give groups a chance to discuss possible solutions, work through computations, and address issues on their own. Then after some “work time/thinking time,” I’m going to talk to the groups of students. I’m going to hear what they have to say, and instead of interrupting them with my thinking, I’m going to question them based on what they share. I’m going to remind myself to use prompts like, “why,” or “tell me more.” We’ll see how this goes, but I’m hoping that the change is a good one!
How do you engage in this cyclical teaching process (i.e., teach, think/reflect, make changes, and try again)? What are any benefits or drawbacks you see in doing so? And, on a slightly different note, what advice do you have for me today as I try this updated math problem?I’d love to hear your thoughts!
Aviva – Forever Teaching, Forever Learning, And Forever Trying To Get It Right 🙂
Yes, my brain hurts this morning — in a very, very, very big way! As we continue to inquire in the classroom, my students often tell me that their “brain hurts,” and I see this as a good sign that they’re thinking. I hope that the same is true for me. Now I’m at the point that I need some help, some advice, or maybe just some good hard questions to get me thinking more. 🙂
Last night, I was looking ahead to next week and trying to do some planning with my student teacher. Right now, we’re finishing our Election Campaign Social Studies Inquiry, and the plan was to move to our Bunch of Bills inquiry activity. I was good with this plan … until this morning. You see, this morning, I looked more closely at the next activity, and now I’m questioning if it’s the best thing to do. While our current Election Campaign was just supposed to be about highlighting the issues at the different levels of government, it’s become more than that. Students are offering solutions, as they know that people won’t vote for them without these solutions. As the students offer the solutions then, we can discuss the pros and cons together, and they can then go back and revise their plans. Do the students still need more time proposing solutions to problems then? Yes, I think they do, as these issues are complicated ones, and the solutions need to address the problem as well as the stakeholders involved. The students also need to look at if their solutions lead to more problems, and these are discussions that are consistently coming out of our guided groups.
So what’s my concern?While I think that students would benefit from some more time to explore issues, I don’t know if they need the complex exploration that is outlined in the Bunch of Bills inquiry activity. That’s when I decided to look back through the curriculum expectations — especially the overall ones for this unit. Here are my thoughts:
The students all understand that there are three different levels of government and that all levels of government have different responsibilities.
The students know many examples of these responsibilities, and they can outline examples of overlapping responsibilities.
The students understand that each level of government is involved in various issues, and when dealing with these issues, they need to consider the points of view of the different stakeholders involved.
The students need more opportunities to create questions connected to the disciplines of thinking, and use these questions to guide their research.
The students would benefit from developing questions connected to a specific issue, and spend more time examining solutions to this issue. They need to outline why their suggested solution is the best one for everyone involved.
It’s with this in mind that I’m considering making a change to my Social Studies plan. I wonder if instead of doing the Bunch of Bills activity, I make a list of various issues from the different levels of government. I can pick ones that the students are interested in, while still providing lots of choices. Then students can pick an issue, and generate questions about that issue (especially connecting to “perspective”). They can examine the answers to these questions, and use their new information to suggest a solution to the problem that would address the needs of all stakeholders. We can end with a Challenge Game, where other students can ask questions to get the groups thinking about problems with their solutions and any revisions that need to happen. This will not be a culminating task. It will address student needs, and it does connect to the overall expectations in the curriculum document. Is this the way to go though? What do you think of this revised plan? I welcome all ideas! Thanks!
Aviva (My brain’s feeling a little less sore after some good blogging time! 🙂 )