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Developing and Writing Effective Math Lesson Plans That Work!

We often hear of research based strategies and how to use them in our classrooms. Having worked at two colleges in the past 20 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. 

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 math lesson plans, click on the resource cover. 

Also look at the resource entitled 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 Peacock Lover Who is New (She Also Teaches Science)


Holly's Store Logo
Holly has been teaching for 24 years. She started out teaching high school biology and then moved to middle school science. Her favorite part about teaching is connecting with kids about their interests, their lives, and their passions. Her classroom routines and rituals reflect this. She spends the beginning of every class talking to her students, asking them how their day is going, and what's going on in their life.

The atmosphere in her classroom is laid back, which encourages curiosity. In fact, she decorates her classroom with things she WANTS kids to touch such as feathers, turtle shells, pinecones, taxidermy, terrariums, plants, rocks and minerals, etc. She is very passionate about bringing nature into her classroom because, sadly, so many kids don't experience nature any longer.

This also reflects who she is as a person - a huge nature lover! One of Holly’s hobbies is raising peacocks (she even has purple ones!), and she brings this into her classroom by hatching peacock eggs with her students every spring. (You can see her birds and the class hatches on her Instagram page.) She is also a busy basketball/track/lacrosse mom and a beach lover. And she's really excited because she will hopefully be getting a horse soon - a passion from her youth that she hasn't been able to explore for many, many years.

Holly has two teenagers, a high school sweetheart for a hubby (who is also a middle school science teacher), three dogs (and she's not afraid to admit her German Shepherd is her favorite), two cats, and a bunch of different birds in her flock - currently chickens, peacocks, and pheasants.

Holly has 600 resources in her Teachers Pay Teachers store, Flying Colors Science, and six of them are free. There are more free resources on her website, that are not available on TPT. She only creates resources for secondary science.

Her featured free resource is entitled Science Journals - Science in the News.  At the beginning of the year, Holly has her students set up a composition notebook exclusively dedicated to science news. In the front cover, students glue a list of writing prompts to choose from. In the back cover, they paste a simple rubric. This free download includes the prompt and rubric.

I thought this was such a great idea, I am considering doing this in my remedial college math classes since it will allow my students to discover that math really and truly is used in real life!

Holly's highlighted paid resource is a ScienceCER Worksheet and Data Analysis Practice. There are two ways to assign this activity. 

  1. As Stations - Great for pairs or groups and for getting kids moving around the room! Eight station cards are provided. Each station card has a very brief description of an experiment and a data table. Students complete a claims, evidence and reasoning grid for each of the eight sets of data. A student sheet is included for the students to fill out as they make their way through the stations.
  2.  As a Worksheet - Great for individual student practice! Students read a short description of the experiment and analyze the data to complete a claims, evidence and reasoning for each set of data.
In addition to her Instagram account, Holly has a website where she has many more science resources for sale, and a blog where she posts various articles about science. I especially enjoyed reading the blog article about Pets in the Science Classroom. You will love reading about Sugar, a pet mouse, but try not to cry when you get to the end!