menu   Home Answers Math Games Free Resources Contact Me  

Effective Lesson Plans and Research

We often hear of research based strategies and how to use them in our classrooms. Having worked at two colleges in the past ten years, I have discovered that some who are doing this research have never been in a classroom or taught anyone under the age of 18!  (Sad but True)  Then there are others who truly understand teaching, have done it, and want to make it more effective for everyone. That's the kind of research I am anxious to use.  I came across the Conceptual Development Model while teaching a math methods class to future teachers. It was one of the first research models that I knew would work. 

The Conceptual Development Model involves three stages of learning: 1) concrete or manipulative, 2) pictorial, and 3) the abstract.  The concrete stage involves using hands-on teaching which might involve the use of math manipulatives or real items. Next, the pictorial stage utilizes pictures to represent the real objects or manipulatives. A visual such as a graphic organizer would also fit in this stage. Last, the abstract stage of development entails reading the textbook, using numbers to compute, solving formulas, etc. Let's look at two classroom examples.

Example #1:  You are a first grade teacher who is doing an apple unit.  You decide to have the children graph the apples, sorting them by color.

Concrete:  Using a floor graph, the children use real apples to make the graph.

Pictorial:  The children have pictures of apples that they color and then put on the floor graph.

Abstract:  The children have colored circles which represent the apples.

Example #2:  You are a fifth grade teacher who wants to teach how to find the volume of a cube or rectangular solid.

ConcreteBring a large box into the classroom, a box large enough for the children to climb inside, OR have the students build 3-D objects using multi-link cubes.

PictorialGive the students pictures of 3D objects which are drawn but shows the cubes used to make the solid. Have the students count the cubes to determine the volume.

AbstractHave students use the formula l x w x h to find volume.

Requiring my perspective teachers to think about this model and to use it when planning a math unit dramatically changed the quality of instruction which I observed in the classroom. 

   Writing Lesson Plans
Now that I teach mathphobics on the college level, I am finding this model to be a crucial part of my planning.  Most of my students started math at the abstract level, "Open your books to page...." without any regard to the other two stages of development. Using manipulatives and graphic organizers have changed my students' ability to learn math, and some have even ended the semester by saying, "I like math". Maybe this is a model we should all consider implementing.

If you want more examples and suggestions about using this model to write lesson plans, click on the link below the illustrationIt will take you to Graphing without Paper or Pencil in which is appropriate for grades K-5 and is based on the Conceptual Model of Development: concrete to pictorial to abstract.

A Go Figure Debut for a Teacher from Nevada Who Is New!

Natalie Trouten
Natalie is an elementary teacher from Nevada. That's Nev-a-da, not Nev-ah-da!  (Did you know that “Nevada” is Spanish for snow covered? It is also known as the "Battle Born State" because it achieved statehood during the Civil War.) She has been teaching for 12 years, and currently teaches fifth grade. She describes her teaching style as flexible differentiation.

She is married with three incredible (that's the adjective she uses) children: two boys, ages 19 and 15, and her "baby" girl who she says is 10 but is going on 16. This is her third year as a TPT seller, and she loves the new friends she has made from the TPT site, blogs and Facebook pages! When she is not teaching (or grading papers), she is usually hiding in a corner with a good book.

Natalie has 78 different resources in her Teachers Pay Teachers store, 15 of which are free. One of those free items is a set of Reading Strategy Posters to be used before, during and after reading. It is a great elementary display to remind students of reading strategies such as words with literary and informational text. It is geared for grades 1-5. I have looked at it and feel it is a quality resource worth downloading.

One of Natalie’s paid resources is a 24 page Novel Study
that will work with any novel! (I like generic resources
Paid Resource
that can be used over and over again.) You can use these novel study pages for individual work, as part of literature circles, reader’s workshop or with whole class novels. You can utilize the entire set as a packet or pick and choose what will work best with the particular novel you are using in your classroom.
  • comprehension organizers
  • vocabulary activities
  • journal assignments
  • rubrics
  • reading goals and reflections
Natalie also has a blog called It’s Elementary. I personally checked it out and found some very interesting articles. Why not take a moment and do the same thing, and while you are there become a follower?

Top Ten Reasons for Getting Stuck when Problem Solving

A good process problem uses no set algorithm to find the solution. It requires a variety of processes (problem solving strategies) to find the solution. It is a problem that is easy to understand, is interesting, perhaps even whimsical, and has numbers sufficiently small enough so that lengthy computation is unnecessary.

Standard Word Problem: Jack's family plans to rent a camping trailer for vacation. The rent is $22.50 a day. What will it cost to rent the camping trailer for one week?

A Problem that Requires Problem Solving: Drew and Addie are playing a game. At the end of each game, the loser gives the winner a chip. When they are done playing several games, Drew has won three games, but Addie has three more chips than she had when the game began. How many games did Drew and Addie play?

So what happens when your students try to do the process problem above and they have no idea what to do? In my last posting, I listed ten reasons why students get stuck when problem solving. Now let's consider why students get stuck in the first place.

Top Ten Reasons for Getting Stuck in the First Place:
  1. You tried to rush through the problem without thinking.
  2. You did not read the problem carefully.
  3. You don't know what the problem is asking for.
  4. You don't have enough information.
  5. You are looking for an answer that the problem isn't asking for.
  6. The strategy you are using doesn't work for this particular problem.
  7. You are not applying or using your strategy correctly.
  8. You failed to combine your strategy with another strategy.
  9. The problem has more than one answer.
  10. The problem cannot be solved.

Since students today tend to be more visual than anything else, a graphic organizer becomes a valuable math tool. The Triangular Graphic Organizer is generic so that it can be used to solve all kinds of formula problems such as: d=rt, A=lw, or c= a2 + b2. 

This five page handout explains in detail how to use the graphic organizer. It also contains several examples as well as a page of blank triangular graphic organizers to copy and use in your classroom.

Want the answer to the process problem? 

Check out the page above entitled: Answers to Problems.

Earth Day - A Time to turn Trash into Treasure

With Earth Day just around the corner, I began thinking, "What sort of extraordinary things could I create from ordinary things which might otherwise be thrown away?"  Here is just one of my Trash to Treasure ideas.

Go to any Quick Trip or a store similar to that and ask if you could have some plastic cup lids, two for each child.  (Stores are usually happy to help out teachers.)  I like the sturdy 4" red ones.  Instead of placing a straw in the designated spot, place a brad to connect two of the lids.  These should be touching each other top to top or flat side to flat side.

After the lids are together, place a few stickers on the outside of the lids.  What do you have?  A card holder!  Just slide the game cards in between the two lids, and they will actually stay there!  These are great for little hands which have difficulty holding several cards, or for older hands which aren't functioning like they use to, or for disabled or crippled hands.  My grandchildren love them because they can now play Old Maid without dropping and showing everyone all of their cards.

Free Resource
Also, go to my store and download a free version of my resource entitled Trash to Treasure.  It is an eight page handout that features clever ideas, fun and engaging mini-lessons in addition to cute and easy-to-construct crafts made from recycled or common, everyday items. In this resource, discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom.

Do you have a Trash to Treasure idea?  Share it with us by leaving a comment.