It’s almost 10:30, and I really should be getting ready for bed, but I can’t sleep. My mind’s focused on math. After working with the students in groups today and reflecting on our discussions, I know that we need to spend more time working on number recognition and counting skills.
- Many students have the rote skills, but they’re not applying their knowledge when presented with various problems.
- Most students can show me their completed work, but struggle with explaining their thinking.
- Most students cannot use what they’ve done to help them with similar problems.
- While students have some number recognition and counting skills, almost all of them do not have a strong understanding of “number sense.”
Based on my assessment,
- I know that students need lots of opportunities to talk about numbers.
- I know that students need lots of opportunities to count groups of objects in various ways.
- I know that students need to look and find different numbers, and we need to work on building this recognition of them.
- I know that students need to discuss their thinking behind what they do, and apply their learning as they work through other math problems.
But this is where I’m stuck. I have a classroom full and pod full of math manipulatives. I have lots of math game options. I have binders full of worksheets that I could use. I know that students need to develop their skills, and I know that there’s value in many of the tools in the classroom, the cupboard, and the pod. All of this being said though, I can’t help but think back to the numerous conversations that I’ve had online and offline about meaningful math, real-world math, and the importance of building thinking skills in math. These tools and activities may build knowledge, but will they help students understand the meaning behind the math?
I need students to see math as more than just something that they do in class each day. I need them to see the connection to their lives, and I need them to move beyond the rote skills to rational learning. With this in mind, I created three different problems connected to real-world examples (one on math in the environment, one on math and construction, and one on math and baking), which will hopefully allow students to practice counting, talk math, and think about the choices that they make. Some of these problems align with the ideas in Cathy Fosnot’s Contexts For Learning resources, which I’ve used. These activities will hopefully allow for us to extend this learning. I’m hopeful that after our math activities tomorrow, maybe I’ll get a better night’s sleep. 🙂 How do you balance the need to practice skills and apply knowledge? How do you make math meaningful while also meeting diverse student needs? I’d love to hear your thoughts on this!
Perhaps all of us need to start thinking about mathematics throughout the entire 300 minutes of instructional time during the day rather than the fragmented block we name as ‘math period’?
Perhaps we need to explicitly look for math all day and in each moment?
Perhaps it is time to think of the day as filled with MATH learning with literacy embedded…..stop spending time pretending we’re teaching ‘making connections’ and ‘inference’ as isolated skills (which they already naturally possess) and start looking at each encounter as a mathematical opportunity.
Step One: marinade them in card games, puzzles, wooden blocks and board games….seems simple but so engaging and mathematical in nature. A simple game of ‘war’ or ‘snap’ or ‘go fish’ will yield high results. Puzzles: spatial reasoning. Blocks: geometry, measurement. Board games: numerical flexibility and application.
Our collective aim: find the math everywhere and always 🙂
Thanks for your comment! Now after thinking math all evening, I was dreaming math all night long. 🙂 The truth is that even though I have a two period math block, math constantly makes it into other parts of our day. While my students will frequently write, read, talk, and create on topics such as shapes and patterns, the same isn’t true for number sense topics. I wonder if some number books might be a good provocation for students creating their own. I can see the social and counting value in the games, but I’m trying to think about how they link with the reading and writing activities that the students often engage in during the rest of the day. Based on their needs, they really need this literacy block that’s high in reading and writing opportunities (and yes, oral language links with these topics as it does with the math one, but it’s trying to find the balance of everything). I wonder if I could write instructions that might allow for reading and math to occur through the games themselves. Maybe this would help students see all of the different things that we can read. I could see the instruction writing link to Language, but I also see the students getting so immersed in the playing and building that the instructions never get written. They really need this writing practice too. I’m trying to think if there’s a way to do both based on student needs in Math and Language. Any suggestions?
Thanks for getting me thinking even more!
Embedding Math naturally in other subject areas and throughout the day is key! We are beginning to inquire how we can embed Math Number concepts into our Science unit on Air and Water. This unit will also make good connections to graphing and 3d shapes as we begin to design and construct various weather instruments. We are beginning to discover, more and more, the need to have a greater cross curricular approach to teaching and learning as opposed to 30 or 40 minute blocks of “just Math” or “just Language”, etc….
Thanks for the comment, Stephanie! The funny thing is that I don’t teach period-by-period or subject-by-subject, but based on my student needs, I’ve created a large literacy and a large math block. Both literacy and math make their way into the other blocks. As I mentioned in my reply to @Nmcfdelk, my students will often read and write about topics such as shapes and patterns, but not Number Sense ones. Maybe the link is through Science. I’m trying to balance the oral language and math needs with the reading and writing needs, and I want to embed math in language more in such a way that it will not detract from the reading and writing time that my students need. What would you suggest? I think I have some more thinking to do. 🙂
I read your blog before bed last night and it stayed with me. Two books come to mind: “Number Talks” is a book I’m taking a look at with some colleagues: http://store.mathsolutions.com/product-info.php?Number-Talks-pid270.html. Another is a Debbie Diller “Math Work Stations” that encourages math manipulative use differently – putting some in bins for games. I’m thinking math games (cards, dice, etc) are a great way to imprint some number skills (like recognizing numbers). While the games are not authentic, playing games is how kids learn. What about “Go Fish Ten” – instead of pairs, make groups of ten for instance? Keep modelling your own thinking – do “think alouds” with math problems. A coach colleague is developing a shared reading lesson using math problems for instance. A few ideas… Hope one or two help 🙂
Thanks for the ideas, Jen! I’ve read Diller’s book before and I’ll check out the other one that you’re reading. I appreciate the suggestion!
I can’t help but think back to a conversation that I had last year with my previous vice principal, Kristi. We spoke about the use of games in the classroom, and I think it was my thinking after that around real world math that is making me struggle with the games. As Jonathan suggested, possibly what I need here is balance … and ensuring that I get that thinking and “math talk” regardless.
I like the comments that others have suggested. The number talks is really good for mental math and practise. Fosnot calls them string lessons.
I was also thinking dot plates are really good for subitizing, lots of math games, if you need them Let me know.
I was also thinking about a food drive problem, where studenTs have to count items to be boxed. Ten items per box. This way they get an idea of ten frames, place value and counting. Plus they start to understand problems outside of there own lives.
I find that teaching through problem solving gives a lot of practise and then You tie in those games and you have a perfect balance; at least in my opinion. Hope that helps.
Your comment reminded me of a number activity we do after Halloween. We ask the children to sort their treats into different groups I.e. Chips, lollipops, loose candy, etc…..and then practice counting how much they got. We suggest to parents that they have their child practice counting in a variety of ways to show them that they will get the same result no matter how they count. Of course, this activity then leads into graphing our results. Real life math experiences and the children just love it!
Thanks for the idea, Stephanie! I know that my students are very excited about Halloween, so this might be a good connection for them too. Students could also do it at home as they count their own treats … and even see what happens to the number, the more they eat (real world subtraction 🙂 ).
Thanks for the comment and suggestions, Jonathan! I have a number of 10-frame activities, but I’d welcome any more suggestions. I keep thinking about a discussion that I had with my former vice principal about games, and I think that it’s impacting on the choices I’m making. Maybe balance is the key. I like your suggestion about the food drive. Based on my current situation, I may bring in some different canned food items or even work with a similar problem. I do like the real world 10-frame idea. It makes me think about planting flowers.
Thanks for getting me thinking some more!
Was that discussion good or bad? Games for me are more then just games. They are in the selfs a problem. They teach the numeracy and the social/communication skills needed for solving mathematics. When children are playing the games I am assessing their thinking, what strategy they are using and where their next steps should be. Then the problems that I do the next day revolve around these outcomes. Just thought I would push games a little more in case it was a negative experience.
Thanks for replying again, Jonathan! I definitely see your point. I’d kind of like to talk to Kristi more about this. Our discussion actually revolved around students making games, and maybe the thinking is more in the playing of them. Maybe the balance with the real world problems is the key. I see both sides of this.
Thanks for giving me more to think about!