Some Reflections on the First Quarter

So, I simultaneously feeling like the first quarter cannot already be over, and feel that August was a very long time ago.  Is this how every year feels, or is this a first year teaching thing?  Maybe a little bit of both.

I also alternate between thinking I am doing well and keeping up and that I couldn’t be more behind and we will never cover everything we need to.  I even feel like I am moving too fast i my Algebra I class, although I think polynomials are going to be a huge hurdle for these students, so I don’t think I will run out of content.  Again, there is probably some of this that will be true every year, but there will also be some of this that will get easier as I go.

I was reading the great Justin Aion’s Blog and he was talking about wanting students to be self-directed and self-assessing, and I assumed much the same things this year.  Of course the students will ask questions if they don’t understand something, I mean, that’s what I would do, right?  But, alas, I have found some of the same issues.  If students don’t really understand something they have just been going with the flow and then getting 36% on a test, which is then my fault when the parent can’t understand why their student did not do well.  I took a step back and realized that what I thought was an opportunity for students to think and learn, the students just thought was marking problems right and wrong on their homework.  I realized that I need more direct assessments for them, so I have been doing more quick quizzes at the beginning of class instead of problem solving and brain teasing, which is sad to me, but seems necessary for now.

In my first quarter of teaching, I also have a new least favorite phrase: “What was the answer to number ____ again.”  As I stated above, I see homework as a time for them to learn and think.  I even believe this about checking homework.  I ask them for questions on their homework, and then I have each students read an answer so that I can see if they have it done, and if we have differing answers, we can explore how different people got those answers.  I also often ask students to come write some answers (especially graphs and number lines) on the board and we evaluate errors and correct answers.  With all of this being said, if someone asks a questions on a problem or we have a disagreement over an answer and I dedicate minutes of classtime to having a student walk me through a problem, I lose it when a few answers later someone asks the answer to the problem we just worked.  This just shows me that they’re checking out, and only really care about getting the right answer.  I have also found that some of the students have realized the game, and if they count ahead, they don’t have to do their homework, as long as they can answer one problem on the spot pretty quickly.  I am still working on the best way to check homework (again because I see this as a learning an thinking opportunity, I only check completion) while also making the best use of my classtime.

Other than that I think I have settled in well.  I need to get a little more organized.  I need to be a little less helpful and a little more questioning, but I think I am getting better at that.  I hope to keep getting ideas and support out of the MTBoS and giving back to it in whatever little ways I can.

The Good and the Not So Good

The Good:

I was working with my students on Visual Patterns 102 as a warm up in class on Tuesday.  During my warm-up problems, there are generally a couple of students per class that can find the answer quickly, and others who either take longer or have a hard time understanding them at all.  While I was working this one, students kept giving me answers (129, 430, etc.) to which I usually respond “Why?” and that gets them thinking a little more.  One of my students who generally does not answer my problems raised her hand and said “I don’t know why, but they look like waffles with a bite taken out.”  The class laughed, and she thought it wasn’t particularly helpful, but I said “That’s actually a good observation.  What shape are waffles, generally?”  And as she was saying “square,” I could see others start to square 43, and one of them blurted out “1849” and I looked at the student who had described the waffle and said “Don’t forget to take a bite out” and she responded with 1848.  It  was a cool moment for that student to see an observation that she saw as a throw-away to be the right step to the solution.

The Not So Good:

Had a quiz in my 6th grade classes on Thursday that just did not go well.  I realized while I was reviewing some things with them that the differences between rational and non-rational numbers was just not something they were ready for.  But I was disappointed on their ability to identify the use of addition and multiplication properties and add and subtract negative fractions.  I think they will get the properties stuff, but does anyone have advice on adding and subtracting negative fractions?  I have a couple of ideas, but I have explained the use of improper fractions or dealing with whole numbers and fractions separately, but they seem to keep making the same mistakes (like getting a positive whole number and a negative fraction when dealing with them separately, but just putting those together and calling it their answer).

One other request for ideas: How do you get students to check for reasonableness in answers?  I ask them if their answer is reasonable when they offer it for the class, and I preach reasonableness of answers (this is actually how I teach decimal multiplication, not by counting decimal places, but by simply asking which whole number do you think this is closest to), but I get quizzes where 3.45+6.45 is 7.9.

Introduction and the Amazing Expanding Expression

Hello #MTBoS!  My name is Sebastian Speer and I teach at a private school in northwest Florida.  I teach accelerated 6th, 7th, and 8th grade math courses.  I have always been interested in teaching and working in education, but I took a circuitous path to getting to math education.

My undergraduate degree is actually in music and I am a classically trained clarinet player.  I realized teaching band was not for me, and I ended up working jobs in a high school and a university after I finished my undergrad.  I have always had a propensity for math, and through those jobs I saw how important the understanding of math was to students’ futures, so I decided to look into becoming a math teacher.  A few years of graduate classes later and here I am in my first year of teaching.  My favorite thing about teaching is the “ah ha” moments when you see a student go from “I totally don’t get this,” to “It all makes sense now.”


Amazing Expanding Expression

I am writing this post, at least partially, for mission one on Explore Math TwitterBlogoSphere, so I am also going to include what I consider to be a “rich task” that I did with my 6th and 7th grade students this year.  I call it the Amazing Expanding Expression.  I use this to work with Order of Operations, so that they can see how extra operations change the value of an expression, as opposed to simply being told they did the order wrong on static expressions on a worksheet.

I begin by writing an expression on the board (the first time we start it’s almost always 4+3.  I don’t know why, but I almost always use 4, 3, and 7 as my examples).  I ask if anyone can evaluate that expression, and then I call on someone.  As long as they give the correct answer, they get to come up and add or change something.  They can put in parentheses, exponents, multiplication, division, addition, or subtraction.  I then ask for any volunteers to solve that expression.

We keep going in turns until the expression just becomes too difficult to deal with.  I then just write a new 2 term expression and we go again.  If someone adds something very strange (divide by 4.736 has come up before), and the other students get stuck, I will usually solve it on the board, and then take my turn in changing or adding something (usually altering it to make it more accessible to more students).

This activity allows students to see how the order of operations affects our answer.  If someone answered 3+4 and added x10 at the end, I will sometimes get the answer of 70 from a student raising their hand.  Another student can correct them by showing how you have to do 4×10 first and you will get 43.

I also like to let them use their calculators on this sometimes, because the people not using calculators often get the correct answers, while those with calculators often get the wrong answer, and this can reinforce my rule of brain first, calculator second.

I look forward to putting more activities and ideas up here and getting feedback.  I am excited to see how this whole MathTwitterBlogoSphere thing can help me become a better teacher.