If you know me well, then you know that one of my best (or perhaps worst, depending upon your perspective) qualities is my insatiability for knowledge. I believe in striving for continuous improvement in all areas of my life, though - admittedly - I am more successful in some areas than others. But ultimately, I couldn't agree more with John Cotton Dana's quote...
That innate push for improvement that compels me to keep going, work harder, do more, and so on, and so on, is what made me perk up when I saw this month's 2getherwearebetter linky theme: Room to Improve. We're doing a little introspection on our last academic year to decide...
(1) What area of your classroom or of your teaching would you like to change or improve in the upcoming school year?
(2) What are your plans for changing it?
(3) Seeking blogger and peer input on others' experiences, advice, and feedback to help us in the process.
Immediately, I knew what my post would be about...WIDA ELD Standard #3: The Language of Mathematics!
Last summer and this summer, I've attended training given by our regional inservice center that focuses on the development of mathematical thinking strategies. I've always considered myself a strong math student, and I've been able to help many of my students with their math practices through the years. But something was missing, especially with the shift toward deeper conceptual thinking that the new standards demand. (Don't get me wrong...I believe in the standards when taught properly as my eyes have been opened through these training experiences. However, it is when someone well-meaning, but - unfortunately - misinformed teaches erroneously...that's the downside. Anyway, that's not the point of this post, so I digress...)
Last summer's focus was on helping students develop additive thinking, and this summer, I enrolled in the next sequential training, which was focused on developing multiplicative thinking. I read and learned so many things that awakened my own mathematical thinking and challenged what I thought I knew about math.
You may be thinking, "Why is an English language teacher attending math training?" Great question! Contrary to popular belief, mathematics is not a universal language. (Again, that's not the point of this post, so I'll save that for another day...) I will suffice it to say that language plays a major role in a student's ability to understand mathematical inputs and to problem solve meaningfully. I have seen this in action in several ways. For example, my English learners sometimes miscount, not because of a lack of understanding of numbers, but because of misunderstanding pronunciation and stress patterns. For example, if you ask an EL to count on from 15, he or she might hear 50, and thus say 51, 52, 53... A well-meaning teacher might mark that child wrong, but the key is separating language-based interferences from number sense interferences. This is just one of many examples of how language can affect performance in math.
So, all that said to say, my area of improvement for the coming year is going to be to focus on developing mathematical language across multiple grade levels with my English learners. I have a great mentor teacher and lots of ideas to start...
A few of the things I learned at training included the importance of incorporating word problems into our children's daily math experiences. Word problems are real life. Period. So many times they are ignored because of the time it takes to complete them, but it is most essential that our students have ample practice with word problems because that's how they will actually be using math in real life! I mean, how many times as an adult have you sat down to a fact fluency test? Okay, okay, sarcasm aside...real world applications are incredibly important. Unfortunately for our ELs, many word problems are unintentionally culturally biased...enter ME! That's an area of language upon which I can capitalize and use word problems to teach them grammar, mathematical vocabulary, and cultural situations in which they might one day find themselves here in the U.S. Take a look at some of the things we discussed in our training... (and my sloppy brainstorms in the margins...LOL!)
That's why when our trainer talked to us about some new strategies for solving word problems and making them a part of regular mathematical discussion, I knew I was hooked. Unfortunately, key words are not a reliable strategy. English has too many inconsistencies, multiple meaning words, and other factors that make key words an ineffective strategy. The mark of a good strategy is its ability to be transferred to other situations, and because key words do not always indicate the same operation 100% of the time, we're letting our students down if this is the only method we teach. So we looked at how to have students generate their own questions from the given information in a word problem, while still withholding the actual problem itself. This gets students thinking mathematically about the information they've been given and all the ways they could possibly manipulate it. Only after you've had a discussion will students be able to see and work the actual problem/question.
I've been really excited about this approach and can't wait to use it in combination with my multiplicative framework and photo problem examples that we also covered at the workshop.
Another area I want to target, specifically with my younger grades, is the true meaning of the equals sign. I noticed while I was helping give our end-of-the-year math benchmarks that first graders were struggling with number sentences presented in any other way but what we might consider "common" or "traditional" (i.e. 2+2=4). If you ask them if 4=2+2 is true, they panicked and told you how that couldn't be true, and when questioned why, they almost all said, "Because you have to write it like this..." and proceeded to show me 2+2=4. This wasn't just an issue with English learners though...this permeated language barriers.
So this summer, I've been testing the waters, so to speak, with some strategies that I might use for this mathematical concept with one of my students. In the pictures below, you'll see how we built up to this process (even though these are upside down, you'll get the idea). I began a few weeks prior to this by introducing the idea to her that equals means "the same as". If that was true, then I could switch my numbers around (as I gave in the example above). We practiced exchanging the word "equals" for the words "the same as" when we read the number sentences. She quickly caught on, so in these pictures, I upped the ante a bit.
We started with one like we had been doing...6=4+2, and she wrote that problem in her notebook. Then I took it a step further by adding a die and questioning her about the new problems. At first, she denied the two sides were equal, but as we wrote number sentences for our dice and checked them, she began to see that they were, in fact, equal or "the same". Then I gave her a few false problems and questioned her. Ultimately, I covered my own eyes and let her make her own problems and try to trick me. (She loved this little twist on trying to trick Ms. Bell!) She really impressed me with her thinking and conversation in this exercise, so I can't wait to try it in a small group when school starts back so we can generate more discussion.
|Testing these two sides to see if they are equal or "the same"|
|Testing these two sides to see if they are equal or "the same"|
|Trying to trick me with identical sides!|
And don't forget to head back over to Schroeder Shenanigans in Second Grade and Lucky Little Learners for the other teachers' posts.