Category Archives: Learning

My Day at Google

I found myself at Google last Friday. A wonderful organization, Ed Tech Teacher, along with Google organized a Jamboree for about 200 educators. We had the opportunity to heGoogle Manar from Googlers (Google employees) as well as amazing technology educators (including Jenny Mageria…check out her blog!).

The last hour of our day was spent listening to a panel of Googlers answer questions. The questions were mostly about the working culture at Google. While some of my colleagues felt as like they were bragging, I heard some really easy things that make an exciting working and learning environment.

1. Everyone’s ideas are heard.

A young software engineer talked extensively about her early weeks on the job. She initially felt intimidated and learned quickly that this was a place where her questions would be heard.  When she asked a question everyone turned to listen to her. This made her realize her opinions mattered.

After Google’s recent decision about Blogger, Google held town meeting style forums for Googlers to ask questions about the decision. The forums lasted for hours and allowed everyone to feel heard.

This takes no money. This is part of a culture where people want to come to work because they feel like they are part of something larger than themselves.

2. You are asked to step outside your comfort zone on a regular basis. You never feel like you know exactly what you are doing.

Several of the Googler talked about being kept on their toes. They are asked to do things that require them to solve problems. Their job descriptions change occasionally and they are constantly learning and growing. In a company setting where you are trying to get the most from your employees it is clear you will get more if they are kept on the verge of comfort. At first this sounds like an awful situation, but after teaching sixth grade math for so many years it is easy to see how this would be a positive. Many teachers teach the same topic and grade level for year after year. There is always a greater learning curve when something is new. The same is true with our students. If we can keep them challenged then we will see more from them.

3. The best way to deal with change is cause it.

The world of technology changes so fast and all the Googlers must keep up with it. They have found that the best way to deal with it is to be on the leading edge. What would this look like outside the walls of a company? It would be children doing great things like this. How do we inspire our students to create and make something better for themselves? How do we get students to stand on our shoulders, use what we know as their teachers, and put it together into something great?

Overall, I had a great day at Google. There are many other takeaways that could be applicable to a education setting. The culture we create in our schools is the culture our students emulate. If we have a culture of collaboration and creation our students begin to mimic it.

 

First Day

September will mark my tenth year teaching in my current school district and my fourteenth year teaching. It is overwhelming to look back at all of the different ways I have started the year. I don’t feel like any of my first days were spectacular. This year things will be different!

I have been doing a lot of reading about the growth mindset. I recently purchased Carol Dweck’s book Mindset:The New Psychology of Success and I think I have the gist. It is all starting to make sense now. I have been trying for years to convince students that making mistakes is the only way to learn and if you aren’t making mistakes you aren’t learning. If you haven’t been reading about the growth mindset and fixed mindset, the premise is that once you believe that your intelligence can’t grow, it can’t (fixed mindset). You need to believe that learning comes from challenges and learn from the mistakes you make along the way (growth mindset). Great! Now that I had some research for these ideas I want a way to start off the year teaching them.

Two years ago I attended the Building Learning Communities Education Conference, while I was there I attended a session where the presenters were doing The Marshmallow Challenge. In the Marshmallow Challenge teams of four are given tape, 20 pieces of spaghetti, string, and a marshmallow. The task is to build the tallest structure that will support the marshmallow in 18 minutes. There is a great TED talk  by Tom Wujec that is also on the website. Tom stresses the importance of just trying something as soon as you have the idea, making a mistake and learning from it.

I’m really excited to start my year this way. I know there’s not a lot of math, but I want to set a tone. I want my students to be ready to accept a challenge, to make mistakes, and to learn.

Tagged , , ,

LCM, GCF, and Fractions.

We had a great time last week working with cogs and I think the mathematical thinking my students did is the kind I want them doing all year. Unfortunately, this lesson is not one of them.

My colleagues and I discussed whether we should even teach these topics. They are definitely not sixth grade topics, but we need somewhere to start and once we start simplifying fractions, we need some common language. I start out by reminding students how they usually find the greatest common factor, by listing out all common factors. I’m always hoping that someone will have a better method, using prime factors, maybe? I then show students the ladder method we used for prime factorization and how it can help us here.

Once again we ask ourselves the same question, “What is the smallest prime that goes into…?”

Using the same method we used for prime factorization we divide out prime common factors. What we are left with is the prime factorization down the left side of the chart, the LCM can be found by multiplying all the outside factors together and there are several other patterns in the chart as well. The bottom factor on the right multiplied by the number on the top left also equal the LCM. Here is the same page with a few completed examples.

There are obvious implications here for finding common denominators. Students can quickly find common denominators and the chart will give the factors that the denominators need to be multiplied by to get to that common denominator. There are a lot of patterns for students to see here and I think it gives a real understanding of how prime numbers can help us work with much larger numbers.

Tagged , ,

Cogs

I was really looking forward to this problem. I couldn’t wait to see what my classes would do with it and it did not disappoint. I mixed up my classes (assigned seats) and gave them very little direction. I wanted to see what kind of mathematical thinking they would do on their own.

nrich.maths.org

The Counting Cogs is very specific and Nrich has even included step-by-step group directions so students can easily manage the problem in a group. Students need to discover which pairs of cogs will allow a colored tooth on one cog to go into every gap on the other cog. Students cut out the cogs, colored one tooth, and started spinning cogs. Nrich even has an interactive that helped me give some classes an idea of what they should be doing. Thank you Nrich for a great problem.

I was thrilled with the thinking. Some students quickly realized they needed some way to keep track of pairs and created great tables and charts. Some students wanted to immediately begin making conjectures. We talked about proving what we believe to be true, and they began to see that one example is not enough to be a proof. Some students even started creating other cogs than the ones supplied to see if their conjecture really worked. I heard a lot of conjectures! Tomorrow when we begin discussing this problem students will quickly discover the cogs that are relatively prime to each other work and the others do not. I did hear this conjecture today, but students just didn’t have enough time to really prove it.

This problem let students extend their thinking about factors, primes, and relatively prime numbers. They were actually applying these concepts rather than completing another worksheet. I really like the way multiple concepts are intertwined in this problem.

Tagged , , ,

Primes

I spent a few summers working in the PROMYS program for teachers at BU a few years ago. You spend the six weeks working with other teachers on number theory topics. Somehow the beauty of number theory had escaped me until this time. Ever since that summer I have really enjoyed teaching prime numbers.

Here are my thoughts on the next week. My sixth graders have seen prime numbers before. I always start teaching it as if they’ve never seen them before. I’m going to have them start by completing a frayer model with four vocabulary words, prime, multiple, factor, and composite. I’m taking the foldable frayer model from here, but we’re not going to fold it.  My thought is once their memories are jogged most students already know these concepts. Why am I reteaching them?

Next up, a little DIVISIBLE Lab. Students once again have seen the divisibility rules in the fifth grade. It drives the faster students crazy when I make them sit and outline all the rules again for the students that have forgotten them. This lab allows students to get up and move around the room. They cannot leave a station until they have the teacher sign off that they are correct. Each letter in DIVISIBLE is a station and students have a lab sheet with questions they complete at each station. I will give students a sheet with all rules written out to keep in their binders after the activity.

Now, the Sieve of Eratosthenes. I used to think it was a waste of time, but I think it is a good activity for students to really see the power of primes. Students go through and cross out all the multiples of two, all the multiples of three, etc. In the end they are left with only the primes. Students then see that there really is no pattern to the primes, that not all odd numbers are primes, all the common misconceptions.

After this, we’ll start prime factorization. I used to teach factor trees, but I had students missing factors when they went to write out the factorization. Last year I tried the box method. Students only have to ask themselves one question, What is the smallest prime that goes in to _________? It looks something like this:

2

24

2

12

2

6

3

3

1

The prime factorization is easy for kids to pull out down the left side. They know when they are done because they get one in the bottom. This makes everyone’s life easier.

Tagged , ,

More PEMDAS

I love being a connected educator. I have learned so much from other teachers in other parts of the world. I just discovered Angie at Coefficients of Determination. She was having the same struggles with the order of operations.

She has created a perfect foldable that I completed with my class this week. They loved it, and I think it finally solidified the order of operations. They are really starting to understand multiplication and division go together and that addition and subtraction go together. Here it is.

Then she played the game risk with them. I had a hard time imagining how this game would work, but I gave it a try and the kids loved it. Check it out.

I’m going to give a quick quiz on the order of operations and then move on. Even my struggling students have an excellent understanding much better than in past years. Thank you everyone!

Tagged , ,

Changes.

This year my room will not look like this. It already looks very different (I don’t have a picture of that). Tables have replaced individual desks and there are working nooks, created for students to work together uninterrupted. Each group will have a large whiteboard for collaborating on problems, a la @bowmanimal, and smaller individual whiteboards for working independently.

Group work has always been the norm in my room. I also feel that students used to be better at it. Now students believe group work is dividing up a problem and copying one student’s work. For group work to be successful there needs to be discussion about the problem before any work is done. I want to spend a lot of time teaching how to do group work at the beginning of the year. There needs to be a lot of processing while students are working. I think Dan Meyer’s beginning of the year activity  stacking styrafoam cups is a great way to start teaching group work. The marshmallow challenge is another idea for teaching group work. While it isn’t directly related to the curriculum, it is a great way to see how students work together. 

Technology! This is the first year that we have laptop carts to share for each grade, as well as projectors, wireless, and document cameras in each room.

1) Class Dojo is at the top of my list. This was a source of conversation at BLC12. The way that you can engage students in a discussion about behavior and what they want the classroom norms to be is very exciting. And who wouldn’t love the little monsters?

2) Edmodo is also going to be implemented this year in my classroom. I was using another website, but I want students to have the opportunity to interact with the site, ask questions, and answer each others questions. I also hope to start posting pencasts to begin flipping my classroom. I say begin, because I am not ready to commit. We’ll see how it goes.

Wow! I didn’t know I had so much to say.

Tagged , , ,