A Tale of Two Teachers

Background:
I was asked to write for my district a curriculum pacing resource guide for second grade during the summer.  A few weeks ago, I saw the stack of worksheets the second grade teachers were planning to use, and I got a bit cranky.  I told them that since I had written their CPR, I should see at least some of the more rigorous activities and lessons in their lesson plans.

Teacher One has been teaching for at least 8 years.  She was not happy when the principal and I told her that the worksheets were unacceptable.   Last week, she came into my office with a baggie of laminated cards, handed them to me, and said, "I don't know what to do with these!  You are going to have to show me."

Since it has been 4 months since I wrote this, I had to ask her to tell me where they came from.  She looked up the web site: http://www.k-5mathteachingresources.com/support-files/skipcountingcards.pdf 

After having my memory refreshed, and sorting out the cards so they were in an understandable order, I was able to show her a few ways that I might use them.

Teacher Two has been teaching for 2 months and came to me after school for some help with her lesson plans.  I asked her what she had planned already, and she pulled up the same activity.  HOWEVER, she told me the ways she was going to incorporate the activity into her lessons.  The only thing that I can honestly say that I added to her lessons was using Two Ways to Count to Ten by Ruby Dee and Susan Meddaugh as an opener for teaching skip counting.

Reflection
Teacher One wants to do activities with her students, while Teacher Two is looking at the learning objectives/targets of her students.  I need to be mindful when I meet with teachers to ask them what they are trying to teach and why, rather than focusing in on the activities. I will especially have to be mindful when working with Teacher One, to help deepen her understanding of what she is teaching rather than going through a series of activities and wondering why her students aren't learning!

Solving Word Problems

The hardest part of my job is having confront teachers.  I hate any kind of conflict and do just about anything to avoid it.  Today I had to address a problem and it turned out positive!

The first teacher has been teaching for about 6 years.  I walked into his class for math, and he had several word problems showing on his SmartBoard.  As the problems were read, he had the students "flashing" their hands when they saw the key word(s) which helped them understand what operation to use.  My heart sank!  No comprehension of the problem, not strategies, just key words!

The worst problem is how do you point something out without the teacher's spirit.  So I did a few things: First, I copied out the article, Caution: Avoid Key Words! from Teaching Student-Centered Mathematics Grades K-3, by John A. Van De Walle and LouAnn H. Lovin, because he and I had already had a discussion about this last year.  I wanted him to see that it wasn't just my personal preference, but that he was going against what was considered best practices.

The next thing we discussed was  the four square problem solving method, UPS-check that we have been doing at the school before he got there.  This is basically a graphic organizer showing the four steps of problem solving by Polya - understand, plan, solve, and check.  I then showed him a video of one of his colleagues leading a lesson with it that I had taken the previous year:

https://youtu.be/CPgX3NTdMCE


His response was that it took her 15 - 20 minutes to solve one problem!  I told him that it is OK for students to work on one good problem during a class period, if the students were learning how to problem solve!  The clincher was when I told him that she had 87% pass rate in math and he had only had 75% pass rate!

I also wanted to give him  a second strategy to give the students, so I showed him the bar method (AKA Singapore Math) which our text series uses.  I even showed him the wonderful web site,  Thinking Blocks  and we went through a few problems.

At the end of the day, he came to me and said that he really had not been teaching key words (I guess blinking the hands at the key words meant something else!).  He was going to start using the UPS-check because the students had learned that last year.  However, he was not going to use the bar method because he didn't know it well enough.

I see that with him I need to encourage him to use more than one representation during his lessons.  I will also have to help him to learn more than one strategy to teach students!

New School Year, New Start!

OK, I'm not great at keeping up with blogs, but I hope that being in this group of mathematics specialists and meeting once a month will encourage me to keep up!

Professional Developments

The first three weeks that I was back at work, I had to deliver five days of professional development!  Three of those days I was presenting on making connections with representations.  The Virginia Department of Education made this easy because they have the PowerPoints and the facilitator's guides for each grade band:  K-2, 3-5, 6-8, Algebra, and Geometry!
http://www.doe.virginia.gov/instruction/mathematics/professional_development/index.shtml

I was presenting the K-2 band, but the people running the first sets of workshops failed to put that into the program, which meant that high school teachers came into my workshop.

During one session, two high school  and one middle school teachers attended.  As we went through the activities I could see that the two gentlemen were increasingly put off with having to go through the activities.  I even overheard one of them say, "They don't need all of this stuff!  They just need to learn the algorithms!"  

I assured him that if he went onto the VDOE website, he could see that ALL students needed to work through the five representations, whether they were in elementary school or high school (or college for that matter!)  I know what the high school scores are like in our district, and I wanted to ask him how his scores were and that perhaps he needed to learn new strategies and representations to increase those scores!  

Albert Einstein said the definition of insanity is doing something over and over again and expecting the same result.

The other high school teacher, I am pleased to say, came to me and said that she could see how these representations could help her students increase their understanding.  We were able to talk for a few minutes and I suggested she look into Dan Meyer's 3 Act Problems  http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/

Introductory Lessons

The first week of school the teachers usually don't get any breaks from their classes during the day.  This is my opportunity to introduce myself to ALL of the students in the school and give the teachers a half hour break.  I also wanted the books to be relevant to the objectives that they will be covering first.  The books I used this year are:

Kindergarten - Ten Flashing Fireflies by Philemon Sturges

Learning Objectives:
Counting to ten


Materials:

• Worksheet with jar
• Counters
• Crayons / Pencils

In the story, children catch the ten fireflies.  As I read it, the children reach in the air to "catch" the next firefly.  We also make a prediction about how many fireflies will be in the jar after the firefly is caught.

When the story is over, the children are given a worksheet with a picture of a jar on it and ten counters - which we call pretend fireflies.  They put some of the counters on their jar and count them.  Then they draw the same number of counters in the jar and, if they know how, write the number of fireflies they drew.

This lesson has been very successful as the students have all stayed engaged.  The biggest problem is that students want to keep drawing fireflies rather than stopping at ten.

The most interesting child's response was one little boy who was struggling with counting.  When I started counting in Spanish, he got a big smile on his face and counted very fluently in Spanish.


1st Grade - So Say the Little Monkeys by Nancy Van Laan

Learning Objectives:
Patterns

Materials:

• Sentence Strips cut in half (12 inches)
• Crayons

FOR THE TEACHER:

• Sentence strips with patterns on it.  Patterns include a color pattern, a position pattern, a shape pattern, and a size pattern.
• Pattern Slide - Made by folding a piece of construction paper in half and stapling it at the top.

In the story monkeys need to build a home, but instead they play.

Before reading the story, I explain to the children that whenever I point to them they are to say "jabba jabba!"  I then read the story, stopping to allow students to make predictions about what the monkeys are going to do.

After the story, we talk about different patterns, starting with "jabba jabba!"  I then clap out a pattern and have them extend the pattern.  Then I start showing my pre-made pattern strips.  I give them two rules

1. No one is allowed to yell out what they think the pattern is.
2. No one can make a prediction about the pattern until they have seen at least four parts of the pattern.

We then discuss all of the different patterns: size, shape, color, directions, and words

The children then go to their desk and create their own pattern.  This gives the teacher a quick assessment about which students are able to make patterns.  Time permitting, I put the students' patterns into the pattern slide and get the students to guess each other's patterns.



2nd Grade:  Two of Everything by Lily Toy Hong

Learning Objective:

• Doubles
• Even Numbers

Materials:

• Two-Sided Counters
• Double Ten Frames
• Ten-sided Number Cubes


• Magic Pot Worksheet

This is a story about an elderly couple who finds a magic pot which doubles everything that is put into it.

The students really enjoy this story, especially when Mrs. and Mr. Haktak fall into the pot and there are two Mr. Haktaks and two Mrs. Haktaks!

After reading the story, we play the Magic Pot Game.  This is played by partners.

1. One person is "Mr. or Mrs. Haktak" and rolls the number cube.  They then put the number of counters that they rolled on one side of the ten frame.
2. The partner is "the Magic Pot" and doubles the number placed on the ten frame.
3. The students record the number rolled, the doubling, and the total number of coins.

I warn the students that if they come to a double they are unsure of, like 8 + 8, they should count the counters rather than guess.  (This has always been a curiosity for me: why students would guess while the answer is easily in front of them!)



3rd - 5th Grade  On the Day You Were Born by Debra Fraiser

This is supposed to be a photo book for parents to put baby pictures in.  As I read this book, we stop to discuss

• what time of day all of the students were born
• where the students were born - I show a map of the United States and show where I was born and then go around the room letting the students share where they were born.  I also have the world map on hand for many of our children
• what season the students were born - I give each student a sticky note and we make a graph showing where the students' birthday are

This graph was made by 3 separate classes.  One class had plain sticky notes, one class put happy faces on their sticky notes and the last group put X's on their sticky notes.

• We then discuss how our bodies have grown and changed over time - I made a PowerPoint with my baby pictures and school pictures, to show them how I have grown (and to prove that I was also a child!)
• The last page states "We are so glad you've come!"  I tell the students that I am glad that they are here, also!

I then give the students a paper for them to first draw a picture of themselves "doing math" and then they are to write about what they like and don't like about math, or what is easy or hard about math.

I think it is going to be a very good year!

The First Day of School

Isn't it amazing that after so many years that the first day of school still causes me to lose sleep!  I could hardly sleep because of the excitement!  The day lived up to the excitement with students and parents coming in droves with bags and bags of school supplies.  Many mothers left their happy kindergarten students with a tear in their eye, or telling themselves out loud, "I promised myself I was not going to cry!"

The cafeteria was a bit of a mess, but because of some fabulous, flexible teachers, the mess was easily resolved.

The only problem ~ not really a problem, but a kernel of a problem.  A teacher, who has difficulty following directions, came and asked me if the district was going to give a diagnostic test.  I told her that I had not heard.  She then asked if she could give her own diagnostic.  This is where the problem occurred.

• I told her that the new math series had a diagnostic test online because another teacher told me about it. But, if the district came out with another diagnostic test, she would be required to give it to her students, and we didn't want to over test the students on the first week of school.

• She said that it would require her to have more computers in her room than she has. 

•  I told her that she could borrow them from the library.

• She then said that she was thinking about a paper pencil test to see where her students were.  She told me that she wanted an end of first grade test.

• I told her that I had the one that we gave last year, and quickly pulled it up on my computer.

• She told me that she saw that one on the internet from another state. 

• I informed her that she didn't, because I made the test myself last year.  I then handed her the printed copy of the test.  I am curious if she will give the test to her class or not.

Here is my problem.  If she was already planning on doing something else, why bother coming to talk with me about it?  IF you come and talk to me about it, why argue about everything?

This was the problem last year, she would try to get ahead of what I was trying to show her team, and then told me she already knew the information, or had a plan.  Her scores showed that she needs to slow down and listen.  How do I say this in a kind and gentle way????

Graphing in the Real World

To get the students to analyze data - real data, I thought I would first show them a line graph comparing the July 2012 temperatures with the July 2013 temperatures.  We have had such a cool, rainy summer this year! It would look like this:

Ask the students what observations they can make from this graph.

Then show this graph which shows what is the average temperatures, and have the students make more observations:

What questions and insights might the students make?  Would there be a conversation about what "average" means?

Counting and Place Value

My rant is over - for now.  Now is the time that I need to start focusing in on what the kids need and what the teachers need to help them meet their needs.

After mulling this over for a few days, this would be the professional development I would give to the teachers the first week of school.

Objectives:
1. Understand the skills necessary to count.
2. Understand the relationship of each place in a place value chart.
3. Understand the importance of teaching using the sequence:

Concrete  - Representational - Abstract

Although they have heard this many times, I don't think they understand the importance - especially when it comes to counting and place value.

1.  If I have a lot of time, I would spend time teaching the "funny numbers" from Kathy Richardson.  This is teaching different names for the numbers 1 - 7.

1.seeze

2.nudge

3.jingle

4.drift

5.ramp

6. groan

7. quiver

The purpose is to get the teachers to be put in the place of the students.  They have to learn unfamiliar vocabulary and attach the numerical value to that vocabulary.  Teachers are asked to come up with statements such as "I have quiver and take away drift, so I have jingle left."

The teachers are then introduced to nonsense symbols related to words ~ This helps them feel the frustrations that the students may be feeling as they are trying to learn sequence, vocabulary, value, and symbols at the same time.

This is excellent, especially for kindergarten teachers who may take for granted that the children know the counting vocabulary and the numerical value of those words.

2.  (This is probably where I would start with the entire staff) Introduce counting in base 5 - done with a document camera.  Teachers would have a similar chart and around 30 counters/unifix cubes.  The finished chart would look like this:

1	2	3	4	10
11	12	13	14	20
21	22	23	24	30
31	32	33	34	40
41	42	43	44	100

Questions to ask:  In the number 32(5) , how would you determine the value of 32(5) in base 10? Can you prove it?

Anticipated Answers:
Teachers will show the 3 groups of 5 and the 2 ones to show 17. 
Some teachers may opt to count on the chart to 32.

Tie in to Teaching:  How did the chart and the manipulatives help you understand base 5 numbers?

2.  Now would be a good time to introduce the place value chart for base 5, asking the teachers to come up with the value of each place:

		25	5	1
			3	2

 Question to ask: What is the relationship between the value of the places?  Can you extend the chart?

At this point, you may be asking yourself, "Isn't this much ado about nothing?  What value is it to learn to count in base 5 or learn the place value of base 5?"

Too many times teachers say that this is easy and they can get through this quickly.  Then there are still fourth and fifth graders that are struggling with place value. 
This is like a professional basketball player telling a six-year-old that making a jump shot is easy.  Of course it is, if you are 7feet 5 inches tall.  It is not that easy when you are 3 feet 4 inches tall!

A 30 year old teacher has been working with place value for at least 22 years.  Of course it should be easy to the teacher!

The finale for this day would be to have the teachers count to 25 using the binary system, and then having them explain the place value of each digit in the binary system.

The exit question/card would be SO WHAT???  What have you learned while working in different bases that helped you?  What manipulatives were useful?  What will you do in your classroom while teaching counting and place value?