Warm-ups in Math Education

Why do warm ups? Is it a waste of time? Is it really worth the bang for our buck?

Let me first start off by stating what I think the importance of using warm ups at the start of a class session. I will use a sports analogy here, for example, before the start of a game, a basketball player will commit some time beforehand to shoot some baskets, cover some drills, go over some plays and stretch! It'd be a foolish thing for the athlete to just jump right in to a game without properly warming up first. In a similar way in math, a student has to be forewarned about what to expect in the upcoming class whether it's a review of something in the past or just reviewing for the sake of reviewing.
Warm ups in math are crucial for students because it allows some time for the students to get settled down and ready to work. I've worked with teachers in the past that gave participation points for students to stay motivated in doing them. Providing warm ups are very simple to implement and does not cost the teacher much energy, money, or time. In my classroom, warm ups will be a form of informal assessment on a daily basis for me where I will strategically ask meaningful, well thought out problems that require critical thinking on my students' end and not just fluff problems that are just to pass the time. These warm ups will not just focus on computation, but the deeper rooted messages that problem solving requires.
Let me now show you an example of a poorly thought out warm up problem and one example of a more deeply thought out problem.

First, "What is the square root of 49?"

While this problem asks the student to regurgitate factual information, it lacks deeper critical thinking skills and does not apply to real life situations.

A better example would be:

A farmer wants to build a fence around part of his yard. He measures the sides which are all equal and there are 4 sides total, and 12 ft each. How much fencing will he need to buy if each foot costs him $5?

Appropriate Use of Technology

The illumination that I selected to talk about is called Turtle Pond. This activity is directed to a K-8 audience and works on basic computer skills along with directional and measurement skills. Basically, the purpose of the illumination is to direct the turtle to the pond filled with nice lilly pads are at nice and safely. On the left hand side of the screen, are some directional arrows that the user can command the turtle to move in any direction. It gets more challenging as you play; where you can add boulders and trees that get in the way of the turtle's path, and you must avoid them to get to the pond.
This game reinforces distance, measurement, and directional skills. It is a very simple game and I do believe that it does a great job of showing kids how to manipulate the directions. However, I would just use it very minimally and in supplement to real manipulatives that are hands-on. The use of this technology does has some advantages over hands-on materials in that it takes up less room and doesn't involve a big mess like blocks or big shapes may have. Another advantage of using the computer as a medium for honing these skills is that many of them will enter possible professions that will require them to have certain computer skills and therefore we are helping to foster some of these basic skills early on in the classroom. Does it take away from the "old school" of learning though? That is an issue that I see more and more today; like we are getting out of touch with fundamentals and relying on technology more and doing less thinking because we entrust a machine to do virtually everything for us. Like stated before, I am not super opposed to using technology in the classroom, but I would just use it as a supplement and not make it a main focus. If I were in charge of this particular lesson, I would use tangible items such as meter sticks, tape measures, and use outdoor objects and have the students go outside to conduct these measurements. It will help them to see actual real life distances and then scaling them down on a screen.

Standards, Standards, Everywhere

As I looked through the 3 different sets of standards online, I got a sense of each one trying to create an individual name for itself, and therefore did not get a sense of unity or having a common goal. As I looked further into each resource, I found that each site was saying practically the same thing but just used a different way of communicating it with the verbage.
The subject area that I researched was in middle school math in the topic of geometry and measurement. In the Common Core standards site, they broke down the topics very clearly and used less formal language to communicate what the students should be able to do at the end of each unit. It didn't necessarily tell the teacher how to present the information which is great I think because it gives teachers flexibility to use whatever activities they want to use. In the NCTM site, the language they used was a little more formal compared to the Common Core resource, but was still understandable for me to interpret. Lastly, in the Connected Math standards, they presented the topics by grade level and associated them with specific workbooks (ones you find at teacher supply stores) that have catchy titles in an attempt to grab students' interest. Overall, each of the standards' sites presented similar topics, but just had their own language to convey their message, and because of the competition aspect of these three resources, I didn't get the feeling of unity that I'd like to see in the education realm; especially when it comes to teaching to standards.