My first tweets! (Exploring MTBoS, mission 2)

So I have had a twitter account for a while. I have never tweeted anything, and I can’t say that I follow anyone either. I have a personal account that I only used to follow @bonnaroo and I have my math account, but neither of which have been tweeted from.

Today I ended the silence streak and tweeted twice! My first tweet was the mini-mission to introduce myself. That sure was hard to do in 140 characters or less! My second tweet hit 3 mini-missions at once (I’m just that good). I tweeted student work, referenced a blog post https://learnsummath.wordpress.com/2013/10/25/math-happenings/ and it was exactly 140 characters.

I think I had never tweeted before because it is out of my comfort zone. I’m not uncomfortable with the technology, I actually love technology, but more so the publicity of it all. I know that sounds silly because I am writing a blog, but I feel like the blog is a little less in your face. I feel like you post things on the blog and if people read it, the read it. The blog for me is more of a reflection on myself, or a venting session for myself, than something I do for others. With twitter I feel like that is something I do to get attention from others. I feel like I am tweeting to talk about myself and get some sort of response from others and I think there is a very thin line between doing this appropriately and doing this annoyingly (kind of like posting status updates on facebook that nobody cares about and are really just annoying.

I am rambling now, so I am just going to stop right here. Maybe these missions from http://exploremtbos.wordpress.com/ will help change my mind about twitter though. We shall see!

I Notice, I wonder

Last year at the Virginia Math Specialist Conference, I sat in on a session led by Cindy Sypolt, who works as  math specialist in Stafford County Public Schools. She shared with us a strategy that promotes making sense of word problems called; I notice, I wonder.

I turned her professional development into one of my own that I used last year. I just did it again this year with my 4th grade team and they seemed to really enjoy it.

We started off by talking about why problem solving is so hard for students/teachers. Much of the discussion was around how it was hard for students to understand the problem, or they rushed through it and didn’t use the right operation. They also said that as a teacher, problem solving is hard because you have to relinquish some control (I wish they would consider relinquishing some control at other times too, but that is a whole different topic for another day).

After a this good discussion, we talked about how “key words” can be misleading for students. They don’t always mean to use the operation that they think they should, and they don’t promote sense making, it’s just a “trick”.

We then made the connection between reading and math and how we value comprehension in reading, rather than just decoding words, and how we should value that in math as well. Just because they can read words on a page, doesn’t mean that it makes sense to them. Why should it be any different for math? Just because they can solve a naked number problem on a page, doesn’t mean it makes sense to them.

Then we went into the notice and wonder strategy. I put up the slide:

Image

and asked them to look at this as if they were their students. Then I asked “What do you notice?”

They came up with things like:

  • there are a lot of words
  • there are a lot of numbers
  • He is buying a sign
  • The enchiladas are cheap
  • You are hiding something from us
  • we don’t know how many veggie enchiladas there are
  • chicken enchiladas were the most sold, 247
  • An Indian person owns a Mexican restaurant

My job was to write down everything they said and not make any judgement, and not guide them in any direction. Then we discussed why this would be helpful to students. They said, among other things, that it is non threatening, it gets them engaged and interested in the story, and starts getting them to pay attention and slow down to think about what they are reading.

Then we moved on to the wonder part

Image

They came up with

Image

(I didn’t have the noticing one at the end so I couldn’t take a picture) Again, I wrote down everything they said. Then I revealed the question and solved the problem.

We had a great discussion about how they could use it in their room with their students, and how they might scaffold it to get students to use it when taking a test. They seemed really excited to have a new strategy to use to help students understand word problems. I am looking forward to hearing if/how they use it in the classroom and hopefully doing the PD with other grade levels.

 

Here is a link to the article that was shared with us at the VMS Conference. I notice I wonder

Math Happenings

Over the summer at a training we read an article called Tying it All Together by Dr. Jennifer Suh. In a very small part of this article she talks about how she got her class to think about math that happens in their everyday lives by reading Math Curse by Jon Scieszka and paying attention to math problems in their life. Although there was a lot of information I was supposed to pay attention to in this article, after I read about this I couldn’t stop thinking about it.

Before the school year started I decided to start a school wide project similar to her idea. I went into all 25 classrooms in my school (Kindergarten through sixth grade). I started off talking to them about where they see math. All of the students usually wanted to talk about the homework they do, or the math their parents have them practice but I tried to guide them to talk about math they might use at the grocery store and in their kitchen, etc. Then I read Math Curse to them and shared a math story from my life and they helped me solve my problem. You can find my full lesson here: Math happenings lesson. (This was pretty difficult with the Kindergartners at the beginning of the year, but I plan on going back in some time this year and doing the lesson again). After I read the book and they helped me solve my problem, I explained that they would be paying attention to the math that happens in their lives this year. When they noticed this math they were going to fill out a Math Happening sheet and I would display them and share them on my bulletin board and share some in the morning announcements. 

photo

I left the students thinking about math that happens and their life and how they could share it with me. I left it up to the teachers to decide when the students were allowed to fill out the math happening sheet, whether during a station or free time, or whether they should do it at home. The students seem pretty excited about it. So far (its been a little less than 2 months into school) I have gotten over a hundred math happenings. Here are a few I have scanned and put into the morning announcements.
mathhappening3 math happening 420131004160108456_0001

“I Do, We Do, You Do”

From what I have seen in teachers using this approach, this phrase means: I show you the process you should follow for a math problem, while you try to memorize it. Then we do the process together to make sure you know how to do my way correctly, and finally you practice the process I taught you on your own. I don’t think this is what is supposed to be meant by I do, we do, you do.

Before I wrote this blog I tried to do a little research about this method, to gain a better understanding, because I thought there was some source out there telling teachers that they should be doing teacher centered instruction and that the best way to teach was to teach students the process of solving certain math problems.

I looked on Amazon to see if I could find any books. I found 1. It was a problem solving book called I Do We Do You Do, An RTI Intervention for Math Problem Solving Grades 1-5 by Sherri Dobbs Santos. I didn’t read the book, but read through what was available in the “look inside” portion on Amazon. The book didn’t show me enough about how the “I do, we do, you do” structure was used but it did lead me toward where their ideas about the structure might have originated from.

In 2008, th National Mathematics Advisory Panel presented Foundations for Success:The Final Report of the National Mathematics Advisory Panel to the President and Secretary of Education. Then they used this information to develop actions that go with it. You can find more information about all of the actions here. I focused my investigation in the teacher resources portion which took me to Doing What Works: Research-based education practices online. Nothing specifically named the I do, we do, you do structure but one of the videos mentioned the I do step very briefly.

From watching many of the videos on that site, and reading about instructional practices in chapter 7 of the report, I was finally able to construct my own definition and thoughts about the I do, we do, you do structure. Usually the I do, we do, you do structure is based on a math concept that they are trying to teach that day. For the sake of this example let’s say that it is addition. The teacher goes over the concept. They review the basics that the students need to think about the concept. For addition they might review what addition means with a basic problem, the vocabulary words that go along with it, add, addition, sum, addend. What they wouldn’t do, or shouldn’t do, is force an algorithm on them.

After the teacher reviews the concept of addition, students have a chance to work together in pairs or groups to solve an addition problem. The teacher is not walking them through the steps, they are discussing how to solve the problem with a peer while the teacher is walking around and checking for understanding. This is the “We do” piece.

After the students have work through some problems together, they should be able to complete problems independently, thus “I do”.

The main focus of this structure is the gradual release. I think, if it is done right, this could have the potential to be a good strategy but I think that many teachers are using it wrong. I think that the name of the strategy should be changed, and that the steps should be slightly different than what is supposed to be done… but that I will save for another blog post.

My Job

My life has been very busy since taking the geometry class that started this blog. I have since finished my masters program at George Mason University, and I am a Title I Math Resource in an elementary school in Fairfax County Virginia. Although I just finished my masters program this spring, I will be starting my third year as a math specialist this fall.

This fall I will be starting at a new school and I am very excited to make this change. In my last school I had the opportunity to work with teachers and students in grades k-6.

My role with teachers was to go to their planning meetings and build their content knowledge, pedagogical knowledge and pedagogical content knowledge. During these meetings I also helped them with creating common assessments and discussing data. Not only did I work with teams of teachers, but I also planned with teachers, co-taught lessons, and modeled instruction. At times throughout the year I also conducted professional development for the staff on mathematics concepts and instruction.

My role with students was very different depending on what grade level and who’s classroom I was working in. In some cases I worked with intervention groups outside of the classroom setting and in some cases I pulled small groups during a guided math structure to work on remediation, or extension objectives.

I enjoyed the role I took on at my last school working in these different ways. I felt like I helped many students, directly working with them, and indirectly working with teachers. Hopefully my role stays similar in my new school!

How do you teach?

In working over the last couple days on this course, we have come across many conversations about the way we teach, and about the way others teach.

I feel extremely lucky to work for the county that I work for. Although it is extremely annoying to always have new initiatives pushed at us it is nice to be ahead of the game in terms of instruction. Two colleagues just attended a DMI math course where they were with other teachers from other areas of the country. They found that many of these teachers boasted about teaching their students to memorize steps to solve mathematics problems. They would brag about special tricks that they would get their students to do. That makes me sad. Don’t teach tricks, teach for understanding!

There are plenty of teachers, even math specialists or math resource teachers, who work in the county who still teach in this way, and even boast about teaching these tricks as well, but for the most part, the county is trying to move away from this. Thank goodness! Our state has not yet adopted common core (unfortunately) but they are beginning to form professional developments around process standards and teaching students to learn conceptually and build their own understanding of mathematics rather than memorizing steps.

Why should we teach in this way? Have you ever had a student that said they didn’t know how to do something, even though you know they have been taught the concept? Well they probably were taught the concept, but they were taught to memorize something, use it for an assessment, cram it back in at the end of the year for the state assessment, and then they didn’t use it for a while so that they forgot it. If we have students make their own generalizations and prove these claims, then continue to use and build on the claims that they know throughout the year and across grade levels, they will be less likely to forget it. For example, you can teach a first grader to memorize doubles plus one facts, but if they come up with their own claim, through repeated exposure, that when you add one to an addend then the sum increases by one (this would obviously be in their own words) they would not only understand doubles plus one better, but they would also understand it when working with other numbers.

Don’t get me wrong, some memorizing is ok (like multiplication facts, as long as they really understand the meaning of multiplication) but I think many people over do it. Maybe there is a reason people teach students to memorize everything. Maybe it’s easier? Maybe teaching the other way is scary? Maybe they don’t know the claims themselves so they don’t know how to get students to come up with it? Who knows…but is that a good enough excuse to deny the best instruction for our students?

Course Development

A fellow math specialist and I are currently developing a course using the book Connecting Arithmetic to Algebra by Russel, Schifter and Bastable published by Heinemann. (Well, we are trying to anyway, our development is often interrupted with passionate discussions about math and instruction) The big ideas of the book are about getting students to make generalizations about mathematics and develop representations to prove their claims. It sounds like stuff you might need in middle school, but it is definitely a book geared toward elementary school math teachers. It is a quick, easy read, and it is very good. I recommend you read it!

In an ideal world every teacher, in every classroom would be able to practice what the book preaches. On a regular basis students discuss with each other what they notice about mathematics and begin to build their own generalizations/claims/rules for arithmetic. Unfortunately in this day and age with standardized testing and specific standards to instruct on, leaving the comfort of a pacing guide to fly by the seat of your pants and have students construct their own understanding can be very scary to teachers. Our goal with creating this course is to help the math specialists, who work in our county, begin to take baby steps toward getting their teachers and students moving forward in this direction.

The authors/publishers of this book, have also created a course guide that can be used with this book, but teachers in our county struggled to make connections to the requirements being asked of them in their instruction, which is why we are developing our own course based off of the book, and using some of the course guide. Our math specialists will be discussing the chapters, solving many math tasks, creating generalizations and proofs, discussing equality, working with teachers and/or students on developing generalizations and proofs and exploring how students can be doing this throughout the curriculum with the challenge of lack of time and the increase of curriculum standards that we are faced with. We will be teaching the course in 4 sessions in the fall/winter of the 2013-2014 school year.

I will keep the blog updated with how to course is progressing and what strides we are making toward the big ideas in this book.

 

 

Exploring additional resources

I work with younger students and I plan on being a math specialist in the future, so I wanted to find resources on plane shapes that I could use with both younger students, and adapt to use with older students.

http://illuminations.nctm.org/ActivityDetail.aspx?ID=35 – is a website from NCTM that is a shape tool. I like this because it can be used with both older and younger students. With my younger students I can have them make pictures, and pair up with a partner to identify the shapes that they used in the picture. They can also use the shapes to make other polygons. With my older students there are tools to do translations.  It can also be used to make tessellations.

http://nlvm.usu.edu/en/nav/frames_asid_277_g_1_t_3.html – is a website from the national library of virtual manipulatives. This site can also be used with younger and older students. Younger students can make and identify shapes and their properties using the geoboards. Older students can be given criteria to make shapes with certain perimeters, areas, symmetry, etc.

http://www.mathplayground.com/matching_shapes.html – is a website where students match shapes to their names. This could also be a good active learning activity for younger students, but a good review activity for older students. Once the matches are made, the properties and attributes of the shapes can be discussed as well as how they are similar and different to each other.

http://www.crickweb.co.uk/assets/resources/flash.php?&file=quad – this website is just a simple sort that students can do putting shapes into categories. It can be an active learning activity for younger students and a quick easy review activity for older students.

Using Tangrams To Understand The Pythagorean Theorem

First I used the smallest triangle in the tangram set and labeled the short sides A and B and the hypotenuse C.

I then used the tangrams to make squares on each side of the triangle.

I used the small triangles as units and found that:

The area of side A = 2 triangles

The area of side B = 2 triangles

The area of side C = 4 triangles

I repeated the process for the medium triangle in the set of tangrams.

For the medium triangle I found that:

The area of side A = 4 triangles

The area of side B = 4 triangles

The area of side C = 8 triangles

Finally I repeated the process again for the largest triangle in the tangram set.

For this triangle I found that:

The area of side A = 8 triangles

The area of side B = 8 triangles

The area of side C = 16 triangles

Usually you would be given the length of the sides of the triangles, but for this problem we find the area first. The area of a square is length x width. Since a squares sides are all the same length, to find its area would be side x side, which is the same as saying A².

I found that the area of each square connected to the triangle was:

Area of A + Area of B = Area of C

small triangle: 2+2=4

medium triangle: 4+4=8

large triangle: 8+8=16

If I were to change this formula into a formula using the length of the sides, which is what a person is most likely given in a problem, it would be:

A² + B² = C²

This activity is a good activity for square roots because students are not usually given the area of the square on the side of a triangle, they are given the length of the side. In this case we have the area, but not the sides. Since we know the area of the triangle is side² the equation for the side would be √area. For each side of each triangle we would need to find the square root of the area. These numbers will also be written as decimals and/or fractions so a good discussion could be had about rational numbers as well.

I think that this would be an excellent activity to use with students. I think I would show them how to make the squares with the smaller triangle and let them repeat the steps with the middle and large triangle. It would be very beneficial to the students learning if they could discuss their findings, and see what conclusions they could come up with on their own. I would group them according to background knowledge on the subject, and facilitate their discussions with guiding questions.

Symmetrical

Line: A figure that matches exactly on both sides of a line

Image from: http://illuminations.nctm.org/lessons/3-5/geometryart/linesofsymmetry.jpg

Rotational: A figure that can be turned and look like the original figure before it is back to the starting position

Image from: http://thesaurus.maths.org/mmkb/media/png/RotationalSymmetry.png