Back in September, I decided to teach my kids how to use the tools of geometry: compasses and protractors. I figured I could give the tutorial in a day and then move on, but the entire experience quickly turned into a mini-nightmare. It turns out that using these tools isn’t as intuitive as I’d thought. They require you to critically analyze a problem to determine what and how to use them, follow a five-to-seven-step process, and then explain your answer. Needless to say, I’ve spent considerably more time this year teaching how to use these tools than I’d anticipated.
If I’m honest with myself, I know that my kids probably won’t need to use a compass or protractor five or ten years down the road. They probably won’t even remember the difference between a compass and a protractor. But they will need to be able to look at a problem, break it down into its components, and use what they know to come to a solution. As a result, I always try to keep in mind that problem-solving and critical thinking are the most enduring things that I can teach them, and that strengthening those skills should be the end goal of any lesson or unit.
This is why I continue to support the Common Core standards: I’ve seen how they empower me to focus on critical-thinking skills with my kids. The standards aim to be “robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers.” I believe that the most important thing the standards do is to empower teachers to teach the skills so necessary in the global economy. I’ve experienced the power of the standards in this regard in three key ways in my classroom.
1) Reduction in number of standards. The Common Core standards dramatically reduce the number of standards that must be taught, freeing up time to push students deeper into concepts—and, in doing so, bring them to deeper levels of understanding.
For example, let’s go back to geometry. Under the old Tennessee Standards, we had more than 120 learning objectives to teach our students each year! Under Common Core, that number has been reduced by two-thirds to approximately 40. Policy makers have done this by streamlining the required objectives, which removes additional secondary subjects—such as probability, which fits in better with algebra and statistics.
This has several implications for a critical-thinking course like geometry. Fewer objectives means I can take the time to present challenging problems to my students, and allow them to struggle with and come to a personal understanding of these concepts over a period of days and weeks. The streamlined objectives mean that I can design my lessons and units to continually draw on previously learned skills to solve problems.
2) Deeper understanding of content. It’s not enough for me to teach my students the equation for a circle—now they have to derive it (i.e., be able to find it) themselves. No longer is it enough for them to simply know what a tangent line is or what it does. Now they must be able to construct one for themselves using geometric tools like protractors, compasses, and rulers.
You might be thinking, OK—how does creating a tangent line equate to critical thinking skills? I was asking myself this very question at the beginning of the year. But this skill requires a considerable amount of background knowledge, as well as an ability to think critically about processes; the ability to self-select and correctly use tools in the appropriate way and in the appropriate situation; and the ability to efficiently and neatly complete a small project. If all these skills aren’t real-world applicable, I don’t know what is.
3) PAARC and Smarter Balance. Under the standards’ accompanying testing consortia, PAARC and Smarter Balance, tests go beyond simply answering A, B, C, or D. They include several new open-response components that require students to explain their thinking. Students receive points for both selecting the correct strategy to solve the problems and for correctly showing their work
And unlike with multiple-choice exams, students are rewarded for their process—even if an answer is incorrect. For example, a student my make one wrong calculation in proving two values equal, but if she can correctly state that the values do not come out to be equal, she may still get points for demonstrating her ability to correctly think critically about the situation. As such, I need to ensure that I am truly teaching my students to think critically about how to solve a problem and present their work.
Does all of this require new standards or new tests to accomplish? Of course not—the best teachers do this every day in their classrooms. But the new format used by PAARC and Smarter Balance provides an accountability mechanism that was not there before. It ensures that all students will be held accountable for not only their answers, but for their thought-process and problem-solving strategies. And this requires that we as teachers teach not only the content, but these skills as well.
The standards are by no means perfect. We should continue to refine them and improve them as they are implemented. But they represent a refreshing departure from the old way of doing things—drill and kill. And they help me to drive my kids toward the higher-order thinking skills that will be required of them later in high school, in college, and in their careers.
By Jon Alfuth
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The standards are not developmentally appropriate for the lower elementary school grades. If followed, they will cause a generation of kids to learn to hate school early.
Also, you point out that these will no longer be multiple choice tests. Have you thought about who will be grading these open response tests and how expensive they will be? That money could be better spent elsewhere, such as on lowering class sizes — a strategy that has been proven to work in research studies.
Interesting that you brought that up as I just finished Malcolm Gladwell’s “David and Goliath.” There’s a whole section in there on how class size reduction is an inverted bell curve, meaning that class size reduction is only helpful to a point and below a certain level it can actually be detrimental to student learning. I’d be interested if you’ve read that book and if you have any thoughts on that.
Huh, I apologize for not publishing that comment. I think that was around the time where I switched to approving comments first and somehow it got lost in the shuffle. I’d love a piece on alternatives to testing that highlights other important areas that might lose out if we myopically focus on tests.
Well, actually, it would be a piece advocating for Opt Out. Would you like that?
I have not read that. I have read the Star study conducted in Tennessee that proved lower income students benefit greatly from class sizes around 16 in the K-2 grades.
http://www.princeton.edu/futureofchildren/publications/docs/05_02_08.pdf
I forget exactly where the cut off is below which students actually start doing worse, but it’s somewhere right around 15 or 16. Shoot me an outline and I’ll take a look
(Whereas, NO studies or even field tests have been conducted on the Common Core to determine whether it is harmful to children’s learning.)
True, and that’s one of my complaints about the way the process has been rolled out (no clear mechanism for modification and improvement of the standards along the way). I’ve also heard some of my colleagues who do make the case that certain individual standards need to be strengthened or removed which is why I think we need to create a way to improve the standards as we go since our policy makes have chosen to implement them this way. Field testing would have been the best way to go, but we’re here now and in my mind this would be the best of the options available to us. I’ll make sure to continue to advocate for such a mechanism in any CC posts I author.
“Back in the day” as a student, I remember complaining about the need for learning particular math concepts. Fortunately my teacher knew more about the need for those concepts. Her patience with me in her class will never be forgotten–today I have to use some of those same basic tools in my small business….I think about her almost daily…you sound like you could have been one of her students who went on to master the subject she knew we needed.
PeggyB.–
Creator of
PrivateSpacers.com
It’s nice that you’re going to protest in articles the need for reform of the CCSS, but I think the solution is open rebellion by teachers. Children shouldn’t be subjected for one minute to standards that are harmful or inappropriate for them.
I guess we will just have to agree to disagree as to the harmfulness and appropriateness of the common core standards
I suppose so. Or you could go observe how CCSS is playing out in an early childhood classroom, do research on early childhood development, and decide that way whether the standards are harmful.
You said you would “advocate for a …mechanism” to change the standards in any common core posts you author, but you didn’t mention the need for this in your most recent post relating to the common core.
Mr. Alfuth, While I admire your wanting to instill “critical thinking” skills in your students, the jury is still out on the Common Core State Standards. When I was in school, it was back in the days right after WWII. I went to school from 1946 to 1959 before graduating from high school. During the 1980s-2000, I think I was a permanent student. I really enjoyed learning the courses that I was interested in. The teachers back then taught phonics in English which prepared students for later courses that required reading. If you can read, you can learn to teach yourself if your teacher can’t. During the late ’70s, early ’80s, major changes came to the classroom. Phonics was out and memorization was in. Biggest mistake made ever. Luckily, my kids made it to high school before that went into effect but my grandkids were told to “memorize” it for the tests. Don’t learn HOW to spell the word, memorize the word as a whole. The US has raised a whole generation of kids who “graduated” out of high school not knowing how to spell but they can read it if they see it. Heaven help them if they can’t see it. Math was changed as well. The kids in today’s classes have so much to memorize, they now have hours of homework to do and the teachers don’t have enough time to teach anymore. They will tell you that the list of things they are required to teach a student in one semester are so much, they no longer have the time to help struggling students catch up. When all the changes went into effect in the ’70’s, it seemed like our school system decided in order to help everyone learn at the same time and “no student left behind” was in, someone in their infinite wisdom (?) DUMBED down the education system in order for all to be passed to the next level. Instead of extra courses to help the disadvantaged learn to stay up with the current students, the students were not taught as much as they should have so the disadvantaged could catch up and stay up. Second biggest mistake ever. Currently, our high school students aren’t ready to go to work in the local companies. Many of them can’t make change for a $20 without looking at the screen on the register that will show them how much to give back to the customer. An example, I went to a local fast food place, ordered and my order was $8.57. I gave the girl at the window a $20 and $.57 in change. She saw the $20 and entered it in the register and it gave her the answer of $11.43, then she saw the change and couldn’t figure out how to credit the .57 and give me $12.00. She had to call her manager over to figure it out for her. He just stared at her and gave me my change. But, I’m quite sure she could have worked out a complicated algebra problem quickly. We need to go back to some better basics in the k-4th grade and teach them how and why to do something instead of just looking at it and not just teach “what” something is.
Thanks for the very well thought out contribution. Again, the point I wanted to highlight is that in my experience, the new CCSS do empower teachers to focus more on these critical thinking skills. You’re right, the jury is still out on the standards holistically. Mine is just one experience of many that I hope will empower teachers to see the potential that exists in these standards.