Merry Christmas Everyone!
I wish you all a very Merry Christmas, and since it is Christmas, I will share an excerpt from my favorite Christmas book. I have made it somewhat of my own personal tradition to read this story every year at Christmas time to anyone who will listen, and I especially love to read the story to children!
“And I thought about the Angel of the Lord–Gladys, with her skinny legs and her dirty sneakers sticking out from under her robe, yelling at all of us, everywhere: ” Hey! Unto you a child is born!” –The Best Christmas Pageant Ever by Barbara Robinson
I hope you will enjoy this story, too!
How Do You Encourage Students’ to Make Sense of Problems and Persevere in Solving Them?
Making Sense of Problems and Persevere in Solving Them is the first of the Eight Mathematical Practices of Common Core. Because this is a practice that needs to be fostered in students and is not easily modeled by teachers, it is one of the more difficult practices to develop in students. Teachers tend not to model problem solving, but they model a method or a strategy to find a solution. Making Sense of Problems and Persevering in Solving them kisses the old “direct modeling” lesson plans goodbye.
Instead of direct modeling, teachers should provide students with rich tasks that help students discover the content they are trying to teach. A good example of this is in one of the TERC math investigations books in which students are given several nets and asked to find the number of cubes needed to fill the net. Students then are asked to make a generalization about how to find the number of cubes needed to fill a net. After this task students devise their own way to calculate the volume of a figure. Students will have different methods to finding the volume of a figure, and this gives place for student voice and higher level questioning and discussion. Then the teacher may lead students into the conventional volume formula after students have found it for themselves.
Instead of direct modeler, the teacher takes on more of a facilitator role. The teacher is responsible for giving students rich, engaging tasks that will guide them into discovering the math content they are trying to teach. Math class then becomes engaging because of its core of students’ discovery through problem solving, and the learning becomes their own. Teachers’ role is to provide students with mathematical vocabulary, notation, and convention to express their found ideas. Teachers should also formatively assess students throughout their learning to gauge the level of challenge that they need to provide for their students. When a teacher becomes skilled at providing rich lessons for the students, then the students persevere because their interest level is heightened.
Cute Winter Door Decoration!
In Celebration I’m Throwing a Sale!
I just wanted to say thank you to all of my visitors. 🙂 I reached the 10,000 visitors mark this week! In celebration of having 10,000 visitors, I am throwing a sale in my Teachers Pay Teachers store the rest of this week through Sunday 12/18/2011. Everything is 20% off!
What’s the Difference in Reasoning Abstractly and Quantitatively?
I recently attended a fabulous professional development which discussed the Eight Mathematical Practices for Common Core Standards. One of these practices is having students reason abstractly and quantitatively. I have always required students to label the answers to their equations when supporting an open ended question, but I didn’t realize the depth of what I was requiring. Consider this. Which is more– 5 or 8? We would all agree that 5<8. This is an example of reasoning abstractly. Now, consider this. Which is more–5 quarters or 8 pennies? We would all agree that 5 quarters > than 8 pennies. This is an example of reasoning quantitatively. When students answer a word problem by labeling each component of their equation, they are reasoning quantitatively. When students merely solve a “naked numbers” problem without labeling the quantities with which they are reasoning , then they are reasoning abstractly. When students are reasoning with specific quantities, then the foundation being built is stronger for them to then build abstractly. Just think. The math textbooks are backwards. Quantitative reasoning problems follow abstract reasoning, however students understanding is built first with quantitative problems and should be followed with abstract understanding.
Do You Need an App for Almost Any Discipline?
Use this link for almost any app you can think of. The link will take you to a nearly exhaustive chart of all types of educational apps sorted by discipline. Some of them are free and some are not. These would be great to compile a list for your students’ parents or to use in the classroom if your school has access to ipods or ipads.
Did Bloom’s Taxonomy Change?
According to a certain website and to the administrators at my school Bloom’s Taxonomy did change. Who knew? Actually Bloom’s understudy Lorin Anderson altered the taxonomy to be more relevant to the current times. This new version of Bloom’s taxonomy has been in place since the 90’s. Synthesis has been removed and Creating has been added as the most difficult level of Bloom’s taxonomy. Also, Anderson changed all of the taxonomy levels into verbs instead of nouns. For example, instead of the Knowledge level, Knowledge has been replaced with the verb Understanding. To view an example of the taxonomy, click here.
Free App for Your iphone to Learn Mental Math Strategies
Our school’s guidance counselor came to me the other day and told me about an app she had discovered on the iphone–Mental Math Ninja. This app teaches mental math strategies using videos all for free. I learned some mental math strategies from watching these videos. Just when I thought I had learned most of the mental math strategies there were from being a math coach and attending many workshops, I learned more! Some of the videos included are:
- Rapidly multiply by 11’s,
- Calculate a 15% tip
- The Secret to Mental Addition
- Rapid Single Column Addition
- Rapid Two Column Addition
- Adding Money
- Rapidly Multiply 2-digit Numbers
- Square Numbers Ending in 5
- Square Numbers in the 50’s
- Square Numbers Close to 100
- Mutiply 2-digit by 1-digit Numbers
- Square any 2-digit Number
- Multiply 3-digit by 1-digit Numbers
- Multiply 3-digit by 2-digit Numbers
- Multiply 3-digit by 3-digit Numbers
- Divide by 0.5 or 5 or 50
My Favorite Christmas Door Decoration
Look at this fabulous stocking (in progress) door decoration! Just in case you can’t tell from the picture, this stocking is completely made from bulletin board paper outlined in heavy black marker. The fuzzy top is composed of white bulletin board paper cut equidistantly every inch or so to hang over the next row. The paper could most likely be curled to add a more dimensional feel. See in the picture below.
Never Underestimate the Power of Anchor Charts
If you have been teaching any time at all, you have multiple Christmas ornaments and other assorted Christmas trinkets from your precious little ones, who are so proud to bring you a wrinkly, wrapped Christmas package. One particular year a student brought me the yellow, glass ball pictured above which beckons the memories of one particular student–Christopher. His sandy, blond hair nearly dangled into his brown eyes. Christopher was intelligent, however he was one of those students when called upon who says, “oh, huh?”. I constantly had to redirect his attention to class discussions and to complete his work. During class one April day after testing I inquired of the class how many feet were in a mile. I must have called on at least 10 students letting them at least have a guess, but none of them coming anywhere close. When I called on Christopher, he said, “5,280”.
I asked, “Wow, Chris, how did you know that?”
He explained, “That chart you used to have there, ” pointing underneath the white board.
The chart Chris was speaking of was one that had been taken down because of testing. I had not put the chart back up, and the writing was very small for him to see from where he was sitting.
I tell this story over and over to teachers to let them know the power of anchor charts on their walls. Students must look somewhere when they are bored and tired of listening to the drone of the teacher’s voice, so they might as well absorb learning from their walled environment. Christopher’s ornament reminds me of this powerful lesson he taught me every time I pull it from the wrinkled tissue it’s wrapped in.
