Monday, June 22, 2015

Differentiation and the Brain -Chapter 1

Chapter 1: The Nonnegotiables of Effective Differentiation

I'm very excited to get started with this book; it's a great topic! So far, it's interesting and a pretty quick read. This is summary of the important ideas in the chapter....sometimes I get a little detailed, because I don't want to miss anything!

In Chapter 1, the authors reinforce the idea that differentiated instruction is not new. (This was discussed in the intro). Though students are in classrooms with others of the same age, students are not "the same." In spite of this, and because of all the material there is to cover, many teachers teach their students as if they are same.
According to research, students will engage more with learning and will learn more robustly when the learning is designed with students' differences (and similarities) in mind. A learner-centered model views the teacher's role as one that is responsible for covering material, but also one that is responsible for maximizing student learning. Whether a student is missing information or has already mastered the current content, a teacher's job is to move each student beyond their current level to ensure that they continue to grow in their knowledge. Differentiation is based on the premise that if a student can't learn efficiently or effectively in one mode, a strong teacher looks for another learning mode that will work.
Sousa and Tomlinson state that the "bedrock of differentiation is a four-part argument that is foundational to effective teaching." Paraphrased, the four parts are:
1) the environment must invite learning - be safe, challenging, supportive
2) teachers should be able to recognize what constitutes essential knowledge, understanding, and skills
3) teachers should "persistently assess student proximity to the essential knowledge, understanding and skills..."
4) when assessment data indicates that a student is confused, has gaps, or has mastered the knowledge, the teacher should use that information to plan future instruction

The authors include a model for differentiation, in diagram form. The diagram describes differentiation as a teacher's response to learner needs; it includes the ideas that shape the teacher's response, names ways to differentiate according to students' factors, and lists a variety of strategies. This is a very detailed and informative diagram....I may need to draw it for myself and hang it in my classroom!

Within the diagram, the five key principles for effective differentiation are as follows (these are described thoroughly in the reading):
1) work in a differentiated classroom is respectful
2) there is a quality curriculum, rooted in the critical ideas of a topic/discipline
3) teachers use flexible grouping on a regular basis
4) teachers use ongoing assessment to guide their instruction
5) the learning environment allows students to feel that they can take risks in learning (this is called building community in the diagram)

The authors end Chapter 1 with the ways in which brain research supports differentiation. These ideas will be discussed more thoroughly in the rest of the book:
1) All brains are organized differently; teaching all students the same way is not brain-compatible.
2) The brain is a "pattern-making machine."
3) Divergent thinking helps to produce new patterns and expand cognitive networks. Differentiation promotes divergent thinking.
4) Emotions play an important role in pattern making; differentiation can offer students more opportunity to reach emotional "aha" moments, which result in chemical releases in the brain and keep learners motivated.
5) Learning is not just a cognitive process, but also a social one; differentiation can provide an environment that is socially nurturing.
6) When information isn't used in a meaningful way, it is not retained in long-term memory. Differentiation can include strategies that make learning more meaningful and memorable.
7) To retain learning, students must be focused and give attention to a topic. The more personally meaningful (through differentiation), the more a student will focus.

In summary, the authors state that differentiation requires teachers to be "mindful" of:
1) how content is structured for meaning
2) who their students are as individuals
3) which classroom elements allow some freedom in connecting content and learners.

Future chapter summaries of this book will be out every few days, on our different blogs: Math Giraffe, The Colorado Classroom, What's New With Leah, and Musings of a History Gal

Check out Chapter 2 here, with Brigid (Math Giraffe)!
Here is Chapter 3, with Brittany at The Colorado Classroom!
Chapter 4 is found here at What's New with Leah!

Differentiation and the Brain - Introduction

It's summer-time and time to get some reading done!
Myself and my Tools for Teaching Teens collaborators are going to read and review Differentiation and the Brain, How Neuroscience Supports the Learner-Friendly Classroom, by David A. Sousa and Carol Ann Tomlinson.We will each be reviewing different chapters, and those blog posts will be linked together as we go. If you're interested in learning more about this book, check back and follow the links to the different chapters:)

I'm going to give a quick review of the book introduction here, and then later today I'll be reviewing Chapter 1.

According to the authors, differentiation is brain-friendly and brain-compatible! They describe the rise, fall, and rise of differentiation, starting with the one-room schoolhouses, where teachers taught all subjects to all students, of all ages, and HAD to differentiate - there was no other way! As the country's population grew, public schools grew, and students were separated into single grades by age, but differentiation was still common. In the 1930s, the industrial model of education began, and the "middle-of-the-road approach" was adopted. Subjects became departmentalized, class sizes grew, secondary teachers became content specialists, and differentiation became less common as the curriculum became one-size-fits-all. In the 1960s, states began exerting more control over schools, and state departments generated curriculum standards and standardized tests. Districts were becoming more alike, but populations in those districts were becoming increasingly different. Testing results showed modest gains, and secondary students scored lower than students in other developed countries, leading to the realization that one-size-fits-all does not work.  As with many aspects of education, we have circled back to the need for differentiation

According to the authors, this book talks about teaching differently and smarter, not harder.
They state that when properly implemented, differentiation emphasizes a shared responsibility between teacher and student. There are many questions this book will answer; the few I am most interested in are:
1) What kind of model can teachers use as a basis for setting up a differentiated and brain-friendly classroom?
2) What are the five major components of a brain-friendly quality curriculum?
3) What are some strategies for effectively managing the differentiated classroom?

I can't wait to get into this book! I hope you are eager to learn what these fantastic authors have to teach!

Click here to continue to Chapter 1.

Monday, June 15, 2015

Puppy Surgery

Summer is finally here, and what I have I been doing? Dentist, doctor, another doctor, and today the vet for my pups. This was not for their regular check-ups (like our human appointments were). Each of them had something to be done.

Oreo had to be tested for Cushing's Disease. If he has this, we will need to start medication for him. His test was pretty easy, and I was able to pick him up a couple hours after I dropped him off.
The vet said he barked quite a bit and had trouble settling down, but after he settled, he took turns sitting on people's laps:) He is blind now (11.5 years old), so I'm sure he was probably a bit frightened without us.

Lily, on the other hand, had to be spayed and she also had a little growth on her gums that needed to be removed. Her surgery went well, but she can't come home until tomorrow:(
Lily looking for me.
The vet told us that during the surgery, she found that Lily's left ovary was 10 times the size it is supposed to be (she showed it to me and I took a picture because I knew my husband would want to see!), so they are going to send that to be biopsied. I'm a little worried about my sweetie.

I think Oreo is missing her already - I know I am!

Sunday, May 31, 2015

A Secondary Summer Not Wasted - Blog Hop!

We are getting close to our last week of school, and I have been trying some different activities with my math classes. Last week, we spent 3 days creating rectangular prisms, to help solve the following problem (this problem is very similar to a problem from a computerized benchmark test...a problem that VERY few students were able to figure out. That problem used a triangular prism; I switched it to a rectangular prism):

Some groups created tiles, others drew them.
"An artist created a rectangular prism covered in square mirror tiles to hang from the ceiling in her studio. The prism's length was 10 inches, the width was 8 inches, and the height was 4 inches.
Find the surface area of the rectangular prism.
Find how many tiles will be needed to cover the entire prism. If the tiles cost $0.35 each, how much did it cost her to cover the entire rectangular prism?"

To solve this, I had the students actually create the prism and somehow show a way to figure out how many tiles would cover it - it was a great activity! They worked hard, they thought hard, they came up with different ways to solve the problem, they were proud of their prisms, and they could really understand both the problem and the solution. They learned quite a bit more than how to figure out the answers, and so did I, which leads me to my thoughts for "A Secondary Summer Not Wasted" -

Lots of rectangular prisms!
encourage students to create/build things!  They don't necessarily need to think about what math they are using, or what other "school skills" they are using. They just need to apply these skills to real situations. During our rectangular prism building, I found that many students don't know how to measure to be sure that their lines are going to be straight. If students spend time during the summer to use math in a practical way, they are not only using specific math skills, but they are also using logic, problem solving, and perseverance, which are so critical to every day success. With some help in the tool area, students can work on building bird houses, garden beds, tree houses, and more! This site, Built by Kids, offers some fantastic projects, complete with material lists and directions, for children of all ages. I have to check out this site more completely to see what my daughter would be interested in.

With guidance and practice, students can spend their summers using math in very practical ways (let's not forget about the use of fractions in cooking/baking - one of my favorite activities!!).

How will you use math in your creations this summer?

Continue on the blog hop to see what The Colorado Classroom has in store for the summer!
Click to go to The Colorado Classroom

Tuesday, May 19, 2015

Discovering Slope

I have never taught slope before. This year is a first for several topics, among which was graphing functions - we did this last week, by using function tables to generate points, and I mentioned positive and negative slopes in passing. In getting more specific about slope, I knew that I didn't want to just tell the students about slope (and about y-intercept) - I wanted them to figure out how the equation of a line can help them understand aspects of the graph of the line. But, I didn't know quite what to do. So, here's what I decided to do: I created a simple worksheet with four equations and their graphs and I simply asked students to find relationships between the numbers (and symbols) in the equations and the graphs of the equations. I didn't give much more direction than that. I had them each think about this, study the equations and graphs, and write their observation on their papers, without discussing with anyone, for about 5 minutes.

Then, I had them choose a partner to discuss their observations with, and to search for more ideas, for about five minutes. As they discussed, I circulated, listened, and asked questions. For the most part, they had written down how the negative/positive sign in front of the x relates to the slope, and many had identified the "added or subtracted number" as the y-intercept. Some had noticed that when the coefficient is higher, the slope of the line is steeper.

Next, I re-paired the students using popsicle sticks, to allow them to share more ideas. At this point, I wrote on the board: "# that is added or subtracted" and "# in front of the x," and asked them to try to figure out what these numbers could tell them about the line (if they hadn't figured it out already).  There weren't many students who made the connection that the slope tells how far to move horizontally and vertically between points, but there were several student whose observation was that the "m" is "how far apart" the points on the line were (they identified the points as where the line crossed the intersection of grid lines - I didn't put points on the lines for them).  After the second pairing, I asked student to write their observations on the board and then we went through and discussed whether they were correct or not.  Then we looked at the same lines graphed on the Smartboard, and we went through what the "m" tells us - we started with the fractional slopes and moved to the whole number slopes.  In all, the entire lesson took about 35 minutes. I was really happy with the students' perseverance (for the most part) in trying to find what I wanted them to find:) I enjoyed their "a-ha" moments!
Click to download

One "mistake" I made in the equations was that both equations with negative slopes also had negative y-intercepts...this led some students to incorrect conclusions, so I changed that for next year. The fixed worksheet is here, if you'd like to use it:)

Today's thinking day is my favorite kind of day:)

Sunday, May 17, 2015

Sailing Into Summer Blog Hop!

I am so excited to be part of the Sailing into Summer Blog Hop! I hope you will "hop" through all the blogs and read the wonderful ideas that everyone has to share! My "fast four" are:

1) One classroom thing I want to do again next year: I did a much better job of using my "Ticket out the Door" poster this year, and I want to be sure to continue that practice next year (and improve it even more).

Click to see on Pinterest

2) One classroom thing I want to change next year: I need to super-organize my materials into binders, as I found on Pinterest (Ms. DeCarbo at Sugar and Spice). I do have my materials in binders already, but I have larger binders that separate materials more by the type of activity than by topic. So I want to reorganize by could take me a while!

Click to see on Pinterest
3) One gift idea for instructional assistants: I have been thinking about this one a lot lately, because my instructional assistant's last day is Thursday. I usually have trouble thinking of cute, unique ideas, so I searched Pinterest, and found this one from "Life is What You Make It." This is a great idea - quick and easy (and useful), which is perfect for me!

4) One classroom organization tip: This may seem basic, but I still have to remind myself to do it every day - put things back where they belong! In the course of my day, I use so many different materials and "accumulate" such a variety of new papers that things can get disorganized very quickly. Immediately putting materials back where they belong and putting new materials in their appropriate place (even if it's the trash can!) helps keep that potential chaos of papers at bay.

Have a fantastic end of the year, and before you sail into summer, check out the rest of the blogs in the blog hop!

Thursday, May 7, 2015

Graphing Functions, with a Freebie

I can't believe it's May already! Time is moving so quickly (as usual), and we are down to about one month left of school!

Our state testing wrapped up and we have started working with function tables and graphing function equations, on a pretty basic level.  We used some practice from our textbook, and the students created functions for each other to graph, but I was feeling that it just wasn't enough practice. I couldn't find anything to suit my needs "exactly," so I decided to make a shorter Footloose activity to give the students some extra practice (along with the movement that Footloose provides).

Click to download for free:)
I created 15 cards that give the directions and the functions. The cards all have the same directions, but they have different functions to graph.

The answer grid for this activity is actually 2 pages - one for students to choose x-values and find ordered pairs using a table and a second one for them to graph the functions. The grids on the graphing page are definitely small, and I was a little worried that they might be too small, but overall, the students had no trouble with the tiny grids. I had one student (out of 125 students) who asked if he could use bigger graph paper, which was fine. The rest of the students did well with the grids.

Before they began choosing x-values for their tables, we talked about the fact that the grids only went up to 10, in both the positive and negative directions. Knowing this, they needed to be careful to choose x-values that would result in the y-values being less than 10. As the students worked, it was interesting to see which students purposely chose negative x-values, to challenge themselves to work with negative numbers (we haven't officially studied operations with negative integers), while others stayed with the comfortable positives.

The students really enjoyed this one!  Feel free to download and use it with your students:)


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