Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Friday, September 13, 2013

Time Traveling


My second graders always surprise me! This week we read a photo essay about a girl who attends a school for deaf students. We learned some hand spelling and signs. We also read a story about Helen Keller. It was after that story that my students began to ask me questions such as:

-Is Helen Keller still alive?
-How old is she?
-Did you know her?



I decided it was a great time to get out one of my magnetic timelines and help them find answers to their questions. I've never taught timelines so early in the year, but I believe in grabbing those natural, teachable moments and riding the "interest wave" as far as I can! This was one of those moments.
Through the course of the lesson, we discussed many things. Here are a few of them:

  • place value and the 1000's place
  • counting by tens above 1000
  • counting on and back on a number line
  • how long ago Helen Keller lived
  • how long she has been gone
  • how old she was when she died
  • whether or not Mrs. Edwards was alive at the same time as Helen Keller (for 13 years!)
  • whether or not Mrs. Edwards knew Helen Keller (It's a big world! and, no, I never met her.)
We now have a foundation to build on as we explore immigration, explorers, and pilgrims later this fall. At the end of the lesson, a student raised his hand and said, "That was like traveling in a time machine!" I think I have them hooked!

Sunday, April 7, 2013

Challenging and Rebuilding Mental Models - Conceptual Models



My students study the road while traveling to the YMCA for swimming lessons. 

Why?

Because they have studied the route, back in the classroom, on Google Earth and are working on their mental map models!

Sometimes we have to break something in order to fix it. When someone visits a doctor for a nose injury, there is a good possibility that their nose will need to be broken again as part of the treatment.

As teachers, we must often go through the process of breaking through the misconceptions and incorrect models that our students have built, in their minds, around an academic concept. These are called mental models. And, we all have them!

What I'm calling a mental model is the representation, or picture, seen, and sometimes "felt," in the mind, when thinking abstractly. For example, the picture you see in your mind when you think about a year divided into months. Is it a line? A circle? A calendar? 

Mental models begin to develop early on in our lives and we test and correct them from then on. By the time my students get to my room, they have all kinds of models that they are using. Many are correct, but some are flawed and can cause problems when learning new concepts. 


Shari's Nerd Corner:

You might be surprised to know that everyone has a slightly different model. What I perceive may not be what you do.

I asked a friend what her model looks like (Yes, I’m nerdy like that!). It took her a minute to understand what I meant but when I asked her to show me where we are right now, (April), she looked down at the place she would put April and pointed at the space in front of her. She described a linear representation that looked like a timeline that repeated every year. When her eyes focused on the space in front of her, I knew she was experiencing what I do. The model is more than a picture. It's an invisible object that she can move and refer to in her mind. 

I suppose my tendency to drift into my Intra-personal Intelligence (Gardner) makes me more aware of these models floating around in my head, but I can't help but notice them! I've been surprised that most people I have asked about their model of a calendar year have taken the time to look and describe it to me. 

The model of a year that I see in my mind looks something like a Ferris Wheel that I travel around during the year. I move counter-clockwise around the wheel as the year goes by. Winter is at the top and summer is at the bottom but don’t ask me for details because the actual visual is a little vague. 

When I mentioned this idea to my sisters last month, one described my model in nearly every detail, which really surprised me, and the other described a timeline model with months in a row. My son describes his as a pie chart. 

What DOES your model look like?

Wednesday, June 20, 2012

Uncle Reuben's Journeys Part 7 - The Camp Out

Once you've finished the hard work of an inquiry project, it’s fun to show someone what you’ve been learning.

We got the chance to do that in early May. The “invitation” group went to work writing notes and inviting other classes to visit us so we could show them what we learned. The afternoon was a success as evidenced by the discussions I could hear around the room as students shared their new learning with excitement.
Language arts activity

Reading with friends in the tent.


One of our favorite pictures of Uncle Reuben is him sitting by a campfire next to a small canvas tent.
I had come across some camping themed math and language arts activities online that would be perfect for a courtyard camp out during the last week of school. We pitched our tent, grabbed something to sit on and headed for the school courtyard for the morning. There were 12 activities to keep the class busy and s’mores for a reward partway through the tasks. It was a nice way to end both our unit and a wonderful 2nd grade year!
Cooler serves as table for story problem work.

Thursday, June 14, 2012

Uncle Reuben's Journeys Part 6 - The Biplane


The chain reached out into the hallway.Keeping the students busy wasn’t too difficult. A group of boys made a chain of colored links the length of the wingspan on the biplane Uncle Reuben learned to fly in 1924. I thought for sure our room would be big enough but once we looked up the size on the internet and the boys got out the measuring wheel, they (and their teacher) realized it wasn’t going to be that easy. Before long, the door was open and the chain was reaching diagonally across the room, out the door and halfway across the hall.

A student is working with the measuring wheel.

They measured, added or subtracted links, and measured again until they were certain the chain was exactly 43 feet and 7 inches.

One concept they learned by doing this is that the chain measured the same if it was straight or curled around the desks.

 A second chain was constructed and measured for the length of the plane (27 feet).


We weren't going to be able to experience the size of the plane in our room so we carried the chains to the courtyard and put them in place.
 The kids and one of their favorite co-op students took their places on the chains and posed for a picture.
Students forming shape of biplane in courtyard.

Note: If you try this yourself, remember that the chain tangles easily and needs to be carried stretched out instead of bunched up. We learned the hard way!

Tuesday, June 12, 2012

Uncle Reuben's Journeys Part 5 - The Time-line




Uncle Reuben lived to be 100 years old; “and 1 month,” a student would usually remind me. What a great number for 2nd graders! Time-lines were being introduced in the math chapter we were working on so we decided to make a timeline display of Reuben’s life. We would be able to develop skills for working with time-lines as well as number lines. I had a few pictures to contribute to the board and stapled a strip of white paper, marked off in 5 year segments, and the pictures to the board for them. A second strip was placed below to represent the 10 years of travel that he did starting in 1924. I then began handing the project over to a group of students.


Every child in the class illustrated some part of Uncle Reuben’s journeys. The group began organizing the pictures. I noticed some girls working with the illustration cards on the carpet one day. Our carpet has a large map of the United States on it. They were placing the illustrations on that giant map and telling the story of his journeys to each other. It was interesting to see what they remembered and whether or not they could find the places on a different type of map. (They could!)

Two students, and several helpers, typed captions for each picture and illustration and those were printed off, cut apart and taped in place. Here is a picture of the finished timeline.

The timeline became a very useful tool and was referred to often when a date would show up in something we were reading.