The Spectacular World Of Secondary Math: March 2015

Saturday, March 21, 2015

Branching Out on Social Media

While I am not anti-technology, I usually prefer face to face contact (or at least voice-to-voice on the phone)! That being said, I realize that I live in the year 2015 and that a social media presence is a necessary means by which to communicate. The odd looks I get from my students when I ask what something is, lead me to do some research and get educated on social media! So, I am pleased to announce that now you cannot only follow The Secondary Math Shop on Pinterest, but also on Twitter and Facebook! I am getting ready to do my first give-away on Facebook when I hit 100 likes and 50 followers on Twitter. I will announce the give-away on Facebook and on Twitter so keep your eyes peeled!

Tuesday, March 10, 2015

Writing In A Middle School Math Class, a Necessary Addition

I love math and writing and when I get the chance to combine the two, I am ecstatically happy! What I am not always best at is coming up with the prompt for students to write about. We have implemented in our math classes a writing tracker assignment twice weekly and an essay each semester. Coming up with a topic once a week is hard enough, twice, well that made my brain hurt! So I did what I always try to do when I am needing something - I turned to TpT. I found the most amazing resource made by Live Love Math - Middle School Math Writing Prompts { Content Specific }. This set includes 70 (seventy!!) writing problems that cover 5 major content standards and are perfect for middle school. I have also used them for my ninth grade algebra class and found them amazing! My students liked the fact that the questions are printed on a half-sheet of paper so that the question is right there and doesn't require them to keep looking up to remember the question. I really enjoyed the fact that the questions could be done in a few minutes and that I had a variety to choose from! I encourage you to check them out!

Sunday, March 8, 2015

More Effective Classroom Discussion and Questioning - How I'm Working to Make it Possible! (part one)

As a teacher you can find yourself in some very uncomfortable positions when standing in front of a classroom full of students, especially pre-teens or teenagers. While you get pretty good at deflecting the inappropriate questions and comments and redirecting students who are heading off on a tangent, if you are anything like me, you still struggle with how to get responses out of students. One of the most uncomfortable moments come when you ask a question and you get cricket eggs. Not even crickets, just simply their eggs waiting to hatch. It's that Ben Stein moment in Ferris Beuller...anyone, anyone, Beuller, Beuller...? You ask, no one answers (or the same students who answers every question shouts something out), you ask again, still no response. Then, nine times out of ten, you end up giving hints or just straight up answering your own question.

In an attempt to combat this, I have spent this year on a quest (in that "free" time that we all don't have) to find more effective ways to facilitate classroom discussion. I started by examining my own question techniques during a lesson to see if changing up HOW I am asking a question has any impact. For example, I changed from asking "Does anyone have any questions" which gives students an out from asking any questions, to "What questions do you have" which assumes that there are questions that need to be answered. This can prod students into thinking about whether they really get it or if there might be something that they are unsure about. I have seen a rise in the amount of questions asked just by this simple change.

Taking into account that fact that many pre-teens and teens really like to "save face" in-front of their peers and not admit to not knowing something I have also expanded on this. I will often ask "If your friend wasn't here today, what question would they have tomorrow" or "Tell me one thing that your friend might be confused about if they just walked in and looked at the board". Both of these questions allow students to have make it seem like it is someone else question and not their own. Additionally, both encourage students to think outside of the box and look at a lesson or topic in a new light. By asking students to put themselves in the brain of another person, they start to examine connections to prior knowledge and make those connections to new knowledge.

The other major change I have made during classroom lessons and discussions is to put forth a concentrated effort to get students talking to each other and working with each other. Once a student has answered one of my questions I will often not tell them if they are right or wrong (mean of me I know!). Instead I will chose one a few different paths for follow.

1) I will ask someone else (or multiple someones) if they are agree or disagree with what the student said which serves multiple purposes. First, it makes students really pay attention to the lesson and discussion since I call on random people not just those with their hands up. Secondly, it makes them listen to each other since they can't explain if they agree or disagree if they don't know what the first student said. Lastly, it helps students to focus their own thinking and understanding to figure out what they believe to be correct or not.

2) I will ask someone to rephrase or expand upon what the student just said. Rephrasing helps students to align their own understanding and to express it more coherently. When I ask students to expand on what was just said, it takes the discussion to the next level and takes a simple answer to a rich mathematical inquiry.

3) I will ask the student to convince me that they are correct. Odd I know, but it makes students take ownership of their answer instead of just saying something for the sake of answering. Additionally, when I go this route, I often find students pulling up prior knowledge, using better vocabulary and often asking if they can come to the board to show me. Other students will chime in to help with the support needed or to correct misconceptions. They love to be right and being given the opportunity to prove it is always a winner!

I don't have all of the answers, but I am seeing positive results so far so I'll keep at it and hopefully continue to improve! Next step, improve discussion during group work and activities! :)

Thursday, March 5, 2015

Graphic Organizers: The What, Why and How of Implementation

Picture this: You are a junior in high school with 6 classes a day, a part-time job, you have a boyfriend or girlfriend and you are vice-president of the student council. Additionally, you have the demands of text messages going off on your phone every four minutes and you really need to sleep at some point. You walk into your 1st hour math class and your teacher casually reminds you that you have a test, tomorrow, on an entire unit of material that was 9 sections long. You have to work tonight and have a paper due for Government in two days! Panicking yet? I know that I would be!

All hope is not lost, however, as your teacher starts handing out a set of graphic organizers that she made ahead of time. These handy little sets of paper include flowcharts, tables, Venn Diagrams and other organizational tools designed to help you summarize the most important parts of the unit. You are start to breath a (small) sigh of relief because at least now you have a place to start and maybe, just maybe, you can still work and study in order to pass the test!

Right Triangles and Trig

For me, I wish graphic organizers has been used, publicized (as I'm sure they must have existed - we just never saw them) and/or encouraged as a study and organizational tool. I had (and still at times have) issues retaining concepts for longer periods of time, partially because I was busy and partially because of how my brain worked. Given that it was 20+ years ago when I was in high school and we didn't have the high stakes standardized testing pressures that students have today, I probably got off easy.

As a teacher at the secondary level, I see what my students have to deal with. It goes beyond the scenario I outlined above to also include studying for the state testing, taking care of younger brothers and sisters, applying for colleges and scholarships and so much more. As a result, I have spent time trying to find a way to help my students be able to better visualize that material, the connections between topics and to help them retain the knowledge beyond a unit test. I want them to develop study skills that will aid them not only in finishing high school but to also help them succeed in college and the workforce. I see graphic organizers as a way to do that for 4 reasons.

Quadrilaterals

1) Graphic organizers are a visual way to "see" relationships. In math so many topics are interrelated but sometimes the relationship can be difficult to see. Through the use of bubbles, rectangles and arrows on a graphic organizer you can see how concepts effect each other. For example, I teach that quadrilaterals form a family tree and teach it in flow chart format. We create a graphic organizer together to show how the properties are "passed down" from one "generation" to the next. My students really start to respond and "get it" once they can see how the quadrilaterals are interrelated.

2) Graphic organizers help students to organize the information in such a way as to highlight and summarize the important concepts. As much as I would love to believe that every word that comes out of my mouth when I am teaching a lesson is pure gold, this is not true. Realistically some of it is just filler, examples or ways of explaining a concept multiple ways to help students understand. It is not always the meat of a topic but the sides dishes as well! Graphic organizers help students to cut through the extra information to get to the foundational parts. For example, when I teach my unit on Right Triangles and Trigonometry, I give my students a set of graphic organizers at the beginning of the unit that they can fill-in as we go along. These organizers are designed for students to include all of the formulas and an example of solving or applying that formula since this is truly the crucial part of the unit.

Transformations

3) Graphic organizers appeal to visual learners. In addition to helping most students see the relationships among topics, graphic organizers can help some students just simply see that information. For some students, notes are just words on paper that they need to try to decode, often without success. Graphic organizers can help them to make sense of those ideas and translate the information into a medium that speaks to them. For example, when we do our unit on Circles, a unit that is extremely visual, my students who learn best visually are known to color coat the parts and constantly refer back to the organizers as they solve problems because they really help them to see, understand and be able to apply the concepts.

Circles

4) Graphic organizers are a tool that students can use to hold on to information long term. If students fill-out the graphic organizers as each unit progresses, then at the end of the semester, they have a great study tool to help them prepare for the final exam. Instead of having to sort through notebooks full of notes or folders full of handouts, they have the most crucial information from the entire semester condensed down to a more manageable number of pages. If the student is truly organized, and can really hold on to the papers long term, they can carry them through prepping for the state testing, entrance exams for college or even on their jobs.

Whatever the reason or method, the course you teach or the level you teach at, I highly recommend implementing graphic organizers into your classes. Not only will your students benefit, but you will too! I have other graphic organizers than the ones listed, please click here to see them all!

Tuesday, March 3, 2015

Ever notice that the internet is flooded with elementary math ideas, but that finding quality secondary materials is virtually impossible.... LOOK NO FURTHER! I'd love to introduce you to the

Secondary Mathletes!

Live.Love.Math - Danielle Krantz

Grades 5 - 9