Monday, May 30, 2016

Number Talk Discussion #8

43 + 9

There are a number of ways to approach this problem. Before we look at them, let's define each term of the addition problem. 
43 and 9 are both called addends.
The answer to the problem (52 in our case) is called the sum.

Round and Adjust

Take and Give

Start From the Left

Break One Addend Apart

Add Up

Did you try a different method? Are some methods more efficient for this problem than others? Share in the comments below!

Friday, May 27, 2016

Wednesday, May 25, 2016

Failure Should be an Option

I recently got my hands on an amazing article by Edward Burger about his experience with grading students in his college courses on their ability to fail.

If students are afraid of making mistakes, it means they are afraid of struggling, of trying something new, of being creative, of thinking in a different way. If grit is the key to success, we teachers are well positioned to nurture the quality.

The fear of failure is a learned one. As teachers, we are often so strapped for time that we don't think spending time on mistakes is a good use of what little time we have; we need to make sure the student can get the right answer so we can move on to the next topic. I think that mistakes allow people an amazing opportunity to ask themselves,  "Why didn't that work? Would it ever work?" Unfortunately, in education we tend to ignore those opportunities and instead focus on getting the correct answer. But then we bemoan our student's inability to think critically or persevere when confronted with something slightly more challenging than the last thing they did.

So what does the research tell us about how to allow students to be incorrect and still use our time efficiently? How do we build in time and opportunities for productive failure? The classroom environment we cultivate can have huge effects. Edward Burger provides his class with an end of course grade for how well each student failed. He asked his students to write a personal reflection essay about their experience with their own failure throughout the course and to give themselves a grade from 0 (did not make any mistakes) to 10 (made lots of mistakes and learned from them). He ended up using the students' own assessment of themselves for their final grade, which counted as 5% of their final grade. The students who received the highest grade were the students who admitted to having moments of failure and were able to reflect on those moments and learn from them. Other teachers have shared personal stories of their own failures and what they learned from those failures at the beginning of the year.

In her book, Rethinking Grading, Cathy Vatterott compares the learning process to being an actor in a play. An actor has many rehearsals (practice) and receives feedback on how to improve their performance during this time. The dress rehearsal (formative assessment) serves to show the actor how close they can come to getting it right. Finally, the actual performance seen by the public, serves as the only thing that "counts," or the thing that gets the grade. She also reminds us that "learning is not error-free - mistakes will be made. If we want to encourage students to view mistakes as a necessary step in learning, we need to remove the threat of grading while they are learning." Instead, she encourages teachers to provide "informative and nonjudgmental" feedback to students during the learning process.

Help create an environment that encourages productive struggle. 
  • Make posters with quotes from famous inventors, athletes, and business people to decorate the classroom. Include quotes about failure and perseverance.
  • Praise students in a way that helps them feel more comfortable making mistakes. Some suggestions include, "Wow, you really practiced that, and look how you've improved." "See, you studied more and your grade on this test is higher." "You tried different strategies and you figured out how to solve the problem." "You stuck to this and now you really understand it."
  • Use feedback instead of grades during the learning process. 
  • If your students ask you a question that you don't know the answer to, tell them, "I don't know, but we can find out!" Let them see what it looks like to not know an answer and what it looks like to discover it.
In past semesters, I have tried a few different ways to elicit incorrect responses from my students, borrowing heavily from great educators such as Dan Meyer and Carol Dweck. I have praised the effort and work my students have put into solving a problem rather than how smart they are. I have presented math problems, and rather than asking for the correct answer, I've asked them for answers they know will be too high or too low, and then asked other students to explain why that particular answer is reasonable. After reading this article, I am excited about creating a culture in my classroom that encourages mistakes and reflection.

What ways have you encouraged your students to be wrong in your classroom in order to help them learn? Share in the comments below!

Monday, May 23, 2016

Number Talk Discussion #7

25 x 16

Break a Factor into Two or More Addends


Factor a Factor

Round a Factor and Adjust

Halving and Doubling

Connecting Arithmetic and Algebra





Did you use a different method to solve this problem? Are some of these methods more or less efficient for this type of problem than others? Share in the comments!

Friday, May 20, 2016

Wednesday, May 18, 2016

Six Assumptions Teachers Make

We all make assumptions about things our students know and don't know. Sometimes these assumptions are correct, and present no problems. Often, however, those assumptions are incorrect and throw off our carefully planned lessons. Today's post is about some of those assumptions, and ways we can slow down and plan differently to help our students and ourselves succeed.

We assume that our students know...
  1. How to behave in class.  No matter what age we are teaching, we tend to assume that our students know how to behave. When students fail to meet behavior expectations, more often than not we respond by sending them out of the room or assigning consequences. While consequences are important, we need to make sure our expectations for behavior are clear and consistently implemented in order to set our students up for success. Taking the time to reteach those expectations after any school breaks, or if things seem to be getting generally out of hand, will ultimately save time in the long run by minimizing disruptive behavior. Additionally, if the expectations you set at the beginning of the year do not seem to be working, you can always change them, as long as you make it clear to the students what changes have been made.
  2. How to take notes.  Children are not born with the ability to take organized notes. This is a skill that is taught to them. No matter how old your students are, assume that they do not know how to take notes, and teach them that skill. I used interactive notebooks in my classroom, and would project exactly what and how the students needed to copy the notes into those notebooks. I taught 6th grade, so there was very little leeway given to my students about how they were to take notes. This worked very well for my classroom. If you teach older students, they might have a method that works especially well for them. If that is the case, allow those students to keep doing what they're doing. However, this will not be true for all of your students, so make sure you set up a method that works for you and teach that to your classes.
  3. How to study.  Because students tend to take disorganized notes, they do not know how to use those notes for future studying. Using lessons to help the students practice using their notes to study is a great use of time. Some ways to set the lesson up could include letting students use their notes to play a game with a partner such as Battleship, Flash Card Flip, Flash Card Match, I Can..., or Task Card Pass. Additionally, you could set up a notes scavenger hunt by creating a crossword puzzle that uses the terms from notes and the definitions as clues. 
  4. How to manage their time.  Many teachers, especially elementary teachers, think that by giving homework they are teaching students time management skills. This is another unfortunate assumption. What ends up happening is the parent's ability to manage their time wisely is tested instead. We can teach students time management skills in a better way by timing activities in our classroom and allowing students to see the timer we are using. Timers can be used for everything from bell ringers, to independent practice time, to bathroom use (if you are a teacher that takes the entire class to the restroom at various times). If students are reading a long passage or solving multiple problems, we can help them by writing on the board where they should be at different time intervals. For example, "In 5 minutes, you should have finished the first paragraph," or "In 6 minutes, you should have completed the first three problems."
  5. How to read on grade level.  Depending on the type of school district you are teaching in, you might have anywhere from 5%-60% of your students reading well below grade level. No matter what subject you teach, we are all reading teachers. Every subject requires students to read, even if it is only the directions. By making sure you are supporting what the ELA teachers are doing in their classrooms, you are also supporting your students and yourself in your own classroom. This support can be as simple as rewriting a text to match the student's reading level, or if the majority of your students struggle, you can close read passages together.
  6. How to solve basic math problems.  Students often enter their middle school years with a poor conceptual understanding of basic mathematical operations such as subtraction, division, and multiplication. This causes many other issues later on, as one might expect. By using manipulatives and illustrations to make the math more concrete, students begin to understand the operations better. While many of us were not taught using manipulatives, or maybe even how to use them in our classrooms, it is worth the time needed to explore them for ourselves and the time needed to allow our students to use them in class. It is a much better use of our time than spending weeks and weeks trying to remediate and reteach concepts later in the year.
  7. How to think about the text or problem being presented to them.  Again, this is a skill that is learned as we grow up, which means that as teachers, it is our responsibility to teach it to our students. We can do this by coaching students to ask themselves questions as they are working on their independent practice. For math, those questions might look like: 1. What information do I know? 2. What am I being asked to find? 3. What operations can I use to solve this problem? For any class that requires reading comprehension, those questions might look like: 1. What is the author telling me here? 2. Are there any hard or important words? 3. What does the author want me to understand? [For literature: 4. How does the author play with language to add to meaning?]
What assumptions have you made that you later realized were incorrect? How did you go about correcting those assumptions? Share in the comments below!



Monday, May 16, 2016

Number Talk Discussion #6

14 x 12

There are a number of ways to approach this problem. Before we look at them, let's define each term of the multiplication problem. 
14 and 12 are both called factors.
The answer to the problem (168 in our case) is called the product.


Break a Factor into Two or More Addends

Factor a Factor

Round a Factor and Adjust

Halving and Doubling

Connecting Arithmetic and Algebra






Did you use a different method to solve this problem? Are some of these methods more or less efficient for this type of problem than others? Share in the comments!

Friday, May 13, 2016

Friday Number Talk #6

Solve the following problem in two ways.

14 x 12

Share your methods in the comments below!

Wednesday, May 11, 2016

Before the First Day of School

As the school year is winding down, now is the time for reflection and self-evaluation. What worked this year? What didn't? What changes would you like to make in your classroom for next year?

If you are about to enter the classroom for the first time, now is the time to start thinking about how you want to set up your room. Looking to other teachers is the best way to figure out what will work and what won't. Talk to veteran teachers about your plan and listen to their feedback. Sometimes our ideas don't actually pan out very well in practice, and this is one of those times where learning from someone else's mistakes is going to make your life much easier.

I've created a checklist to help you get organized and hopefully help reduce stress and feeling overwhelmed by what you need to do before the students walk in on that first day of school.

What are some things you would like to try next year?

What are some things you did this year that worked well for you?

Share in the comments below!


Monday, May 9, 2016

Number Talk Discussion #5

247 - 98

Round the Subtrahend to a Multiple of Ten and Adjust (Katie's method)

Decompose the Subtrahend (a variation of Tommy's methods)

Add Instead

Same Difference

Break Apart by Place


Did you use a different method to solve this problem? Are some of these methods more or less efficient for this type of problem than others? Share in the comments!

Friday, May 6, 2016

Friday Number Talk #5

Solve the following problem in two different ways.

247 - 98

Share your methods in the comments below!

Wednesday, May 4, 2016

Taking Care of Yourself as a Teacher

When you are a teacher, it is easy to lose sight of your own needs. It took me until Spring Break of my third year in the classroom to realize I hadn't been taking care of myself my entire career as a teacher. If I took time off over the weekend to sleep or visit family or go hang out with friends, I felt guilty. I celebrated the first time I went into a store and did not leave with something for my classroom or students with a Facebook post and some delicious Mexican food. This was well into my second year of teaching, and I still remember it vividly.

If you are about to become a teacher, or have been a teacher for years, don't fear. This is not a rant about how hard teaching is or all the burdens we take on in that role. This is a post about the ways you can take care of yourself as a teacher. Or as a human person. Some of these things might seem like common sense, and if they are things you already do, Hooray! Keep doing them! My hope is that I will give you some new ways to take care of yourself during the school year, and every day outside of it as well.

Take Care of Your Health
  • Eat healthy snacks throughout the day.
  • Stay hydrated.
  • Use the restroom when you need to! (Ask another adult to watch your class if you have to. Do the same for others if they ask you.)
  • Take vitamins.
  • Wash your hands, wipe down desks and doorknobs, and use hand sanitizer if soap isn't available. Do this religiously!
  • Get enough sleep. Schedule time for this if you have to. Set alarms on your phone to remind you that it's time for sleep. Sleep is important!!

Take Care of Your Emotional Wellbeing
  • Write (poetry, blog, diary entries, letters, etc.)
  • Read good books (and not just books about teaching!)
  • Go out with friends. Try to go out with friends who aren't teachers occasionally!
  • Make something (cookies, cakes, food, bread, paintings, drawings, pottery, etc.)
  • Watch TV and movies.
  • Go for a walk/run/bike ride.
  • Meditate
  • Go to a counselor regularly (this job is hard, so let someone else help!)
  • Talk to friends and family who aren't nearby
  • Keep a journal at school and document the "moments of win," no matter how small they may seem.
  • Make positive phone calls home and send good notes home with students.
  • Set a work schedule and stick to it. If school lets out at 4, stay until 5 and work. After 5, if it's not finished, you'll get to it tomorrow. If you've scheduled 3 hours for work on Saturday, you only get those 3 hours. After that time is up, you have to go do something else.

Remember
  • Never feel guilty for taking care of yourself first! You cannot be an effective teacher if you are sick or tired or stressed out all the time.
  • Mistakes will be made. Learn from them and move on. Do not strive for perfection, strive for "better than yesterday."

What are some things you do to take care of yourself? Share them below in the comments!

Monday, May 2, 2016

Number Talk Discussion #4

34 - 9


There are a number of ways to approach this problem. Before we look at them, let's define each term of the subtraction problem. 
34 is the minuend. The minuend is the first number in a subtraction problem. The number from which another number is to be subtracted. 
9 is the subtrahend. The subtrahend is the number that is to be subtracted. The second number in a subtraction problem.
The answer to the problem (25 in our case) is called the difference.

Round the Subtrahend to a Multiple of Ten and Adjust

Decompose the Subtrahend

Add Instead
 

Same Difference


Break Apart by Place


Did you use a different method to solve this problem? Share in the comments!