Our task this week is to look at the Georgia Performance Standards for a subject area and evaluate them for critical thinking skills. I'm deviating just a tad from this and looking forward to next year when we will be implementing the Common Core Standards for Mathematics. This is a timely exercise as teachers across the United States are studying this implementation and discussing the impact it will have on our classrooms. Within Georgia, we will have new objectives for each grade K-12. These objectives are being framed by an expectation for a "culture shift" within many of our classrooms. In addition to the very specific objectives, teachers are asked to design lessons and create learning environments that reflect the following Standards for Mathematical Practice.
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
If you look closely at these, you will notice these expectations require the use of critical thinking. This is the basic premise/directive given to teachers before they even examine individual, grade level standards. Wow! In my mind, the bar has been raised and I see critical thinking as an expectation for every student. The individual, specific standards address content objectives while these address "habits of mind".
In the fourth grade Common Core Standards for Math, I found a standard that could be taught using technology and critical thinking:
MCC4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles
For this standard, I would use photographs of architecture to identify parallel and perpendicular lines as well as angles and right triangles. These photographs would be projected onto an interactive whiteboard where the initially the teacher could highlight these. This would be followed by the students using the highlight tool to identify these features in additional photos and defend their choices to the class. Finally, the students would be asked to work in pairs to locate photographs that illustrate each concept.
This activity would cover 1-4 of the standards of practice for Mathematics in addition to meeting the objective for MC C4.G.2.
Carla,
ReplyDeleteI noticed you picked the mathematical practice standards. Those do seem to require some critical thinking. I focused on the actual math standards for the Math 4 course. They were relatively basic. I was disappointed in what they required. It was really drill and practice. So I think it's up to the teacher to really take the mathematical standards adn apply these practice standards and make it a meaningful experience.
Nice post. I'm glad to hear that your standards lend themselves to critical thinking. Your example lesson sounds great. I wonder if you could also have them CREATE their own picture and label the shapes, maybe after they get used to recognizing shapes and lines in other pictures. That way, you can take them one step farther. Good job:)
ReplyDeleteCarla, what a great idea! As Lara commented, I would also like to have students take their own pictures and analyze them according to the features of triangles. I think this would get students more engaged and motivated as well!
ReplyDeleteI like it when standards are tied to the real world. I teach architecture in my classes, and highlight math standards constantly. This is excellent for critical thinking, and helps students see how math is used in the real world and that they will use it. Have you considered using bridges as another type of real world example? They use triangles and beams to transfer force from areas of weakness to areas of strength, and also overlap in the area of physics, and physical science. Great creative thinking, and use of standards.
ReplyDeleteNick...I teach kids that the triangle is the strongest shape and then pull up beams and bridges to illustrate the point. I have pictures of the building I teach in underconstruction...the kids can actually "see" the triangles that are surrounding them and holding our building up. In my next life I will be an architect or designer of bridges :)
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