Part 7 of 8, Strategies for Integrating the Mathematical Practices into Instruction
This mathematical practice involves the ways students can explain to themselves the meaning of a problem and the ways they find to enter into solving it. It might feel like being a detective who is looking for clues or evidence on how to solve a problem. Students proficient with this practice believe they are mathematicians and try several methods to come to a solution.
This blog series will conclude by examining Practice #1 in this post and Practice #6 in the final post. These two practices can be thought of as overarching habits of mind that productive thinkers use as they work with mathematics.
21st Century learners are used to being plugged-in. They crave it. They have been raised in a technology rich environment. When toddlers reach for a phone now, they immediately try to text and swipe, rather than mimicking talking into the device. The times are changing, and your classroom should too.
But what if you don’t have the funding? Maybe your district was hit particularly hard during the recession. Maybe resources are being allocated to special programs like STEM or to magnet sites within your district. Maybe you teach an elective course, and resources are reserved for “core class” instruction. How can you tap into your student’s desire for technology on a tight budget and with limited resources?
What did we ever do before tablets, smart phones, and computers? How on earth did we ever teach students without PowerPoint®, interactive whiteboard, and Google™?
As an online learning teacher, I find it fascinating to think about teaching and student literacy before technology. I believe that, when it is used appropriately, technology can be the key to the kingdom of excellent student literacy.
I have taught high school English Language Arts for 15 years. When I started, I had a desktop computer, and the high school I worked for had one computer lab with 10 computers. The most engaging activity incorporated into teaching literacy at that time in my classroom was gaming. I had games for everything: vocabulary (Race to the Chalkboard Challenge), sentence building (Grammar Gladiators), and comprehension (Sherlock Search).
Look for and Express Regularity in Repeated Reasoning
Part 6 of 8, Strategies for Integrating the Mathematical Practices into Instruction
By Dr. Michele Douglass
Of all the mathematical practices, I find this one hardest to implement. It is probably from my years of being taught how to just manipulate numbers versus how to use patterns to generalize.
This practice reverses the thinking of the previous practice (MP#7). For this practice, we want students to use patterns that we might give them to generalize a situation. For example, instead of teaching rules for adding integers, how could students look at patterns to generalize or come up with the rule? Think about a lesson that has students examining graphs and matching equations in order to generalize the slope-intercept equation.
p>Thank you, educators, for taking the time to submit such well-written and thought-provoking blog entries on the four education topics that we provided. It was a tough process, but we have narrowed the entries down to three finalists. Now it’s your turn to read the entries from the links below and vote for your favorite blog!
To view and vote for you favorite blog submission please go to www.voyagersopriscontest.com.
Good Luck to the finalist!
I pulled my first all-nighter my freshman year of college. My roommate and I had both been assigned to Mr. Seager’s 8 a.m. chemistry class. Mr. Seager was a science whiz who was passionate and knowledgeable about his topic, but he was a lousy teacher. After dozing through many of his uninspired early-morning lectures, Kaye and I had fallen way behind in our understanding of the content. We knew we had to stay up all night and cram.
Up until this point in my life, I had never had a cup of coffee. Both of my parents were British immigrant tea drinkers who believed in serving whole milk to their growing teenagers. But then came college—no rules, no parents, no sleep. And Mr. Seager.
To be fair, Mr. Seager was not atypical of the teachers at many universities. Their practice was to stand at the front of the room, back to the class, as they wrote notes on the board and lectured simultaneously. This type of teaching was fertile soil for dozing students.
I had the opportunity to attend some training last month with a colleague I don’t know very well. I’ve worked in the same building with this teacher for three years now, but I’ve rarely been down to her room. I suppose I had my own assumptions of how good a teacher she was from snippets I’d heard in the hallways from students, but I really had no clear idea who she was as a person. That was my loss.
According to the Megan Meier Foundation, 13 million children will be bullied or cyberbullied in the U.S. this year.
Megan Meier was from O’Fallon, Missouri. When Megan opened an account on MySpace, she received a message from a supposedly 16-year-old boy, “Josh.” They became “friends,” even though they never met or spoke on the phone. “Josh” claimed that he lived nearby and was homeschooled. He did not exist. Lori Drew, the mother of Megan’s former friend Sarah Drew, created him.
Lori was aided by several others and intended to use Megan’s messages to “Josh” to get information about her and later humiliate her, in retribution for her allegedly spreading gossip about Sarah.
Part 5 of 8, Strategies for Integrating the Mathematical Practices into Instruction
Looking for and Making Sense of Structure means using deductive reasoning. In other words, I recognize the pattern and can apply it to solve a specific problem. This is the one practice that I am most often asked about by teachers in primary grades. They want to know what happened to all the standards about patterns. My response is always the same: Math is all about patterns, so it isn’t something that should be taught as a single standard, but rather as a practice that we use when thinking mathematically.
This practice is about how we work with students so that they are always looking for and making sense of repeated structures. For example, a sequence of numbers begins with 5. The next term is found by adding 4, and the next term is found by multiplying by -1. If this pattern continues, what is the 25th term in this sequence? Do you have to write the first 24 terms in order to figure this out? Seeing and using patterns moves beyond the primary standards of the past of recognizing AB or ABBA patterns.
October is Bullying Prevention Awareness Month (www.stopbullying.gov). PBS offers varied useful resources at The Bully Project. This is certainly a fine start, but bully-proofing is no simple task. Collapsing a bullying culture cannot be accomplished in a month or with a single campaign. Constant vigilance is required.
But sometimes teachers don’t see the bullying. Children report it, but when teachers then try to observe it, they see nothing. Shall we stop there? No. That will convey entirely the wrong message.