by Elaine Gallagher 

             My philosophy of teaching is based on respecting the dignity and individuality of each student.

             Recognizing that my students have distinctive ways of learning (Gardner’s Multiple Intelligences), and that teaching needs to provide critical thinking opportunities for the students (based on reaching higher levels of Bloom’s Taxonomy of Cognitive Thought), it is important that I plan each lesson well to include activities that go beyond the book. Activities I use combine several types of intelligences to reach all students. I make sure that my activities arrive at the “Application” level (or higher) on Bloom’s Taxonomy. I also make sure that my activities include visual, auditory, and tactile experiences for the children, not only for little ones, but for older learners, as well.

One example of a successful lesson I taught:

First graders who are learning to add single digit numbers. 

1. Before even opening the book, I will sing a number song with the students, such as “One-two, buckle my shoe…” to put them in the mental framework of “math”, and to begin the new lesson with something they already know.
2. Then, I will have students in groups of 3 or 4 come to the front off the class where I will give them 1 or 2 items each, such as a ruler, pencil, pen, crayon, paper clip, etc.The students in the front will hold up the objects so that the seated students can see them.Then I will guide the students to count the objects, 1,2,3,4,5, etc. asking them to give me a TOTAL number of objects that the group in front      has demonstrated. If there are 8 objects, I will have a student write “8” on the board.
3. REPEAT this activity with each group, only concentrating on the total number, gradually using the term “SUM” as a synonym of “TOTAL”.
4. Once the entire group of students has had the opportunity to be in front and arrive at a total/sum of objects, I will have 2 students come up front, and give them several objects each.
5. This time, when the seated students count the objects shown by the first student (3, for example), the student helper will write 3 on the board.  
6. When the seated students then tell me that the second student has 4 objects (for example), the student helper will write 4 on the board.  
7. I will ask the class to tell me the TOTAL/the SUM of the objects that the two student have shown. They will say” 7”.
8. Then all students are seated…and I will write 3 + 4 = 7.
9. We will discuss what we did, learn the words add/plus/equals/total/ sum.  I will also explain that “equals” means “the same as”, and we will use those words synonymously with “equals”, as: “Three plus four is the same thing as seven.”  OR “Three plus four equals seven.”
10. Once they are able to use these words and exhibit understanding, I will then go to the corresponding pages of the math text to continue with the lesson.
11. I will precede each lesson with a hands-on type of activity such as the previous one.
12. Follow-up activity (perhaps another day): Students will be given several small sheets of colored paper, which they will use to cut out shapes of their choosing, to paste onto a clean sheet which has been divided into 4 sections (folded into quarters). At the bottom of each quarter, the students will copy an addition example that they can choose from their books, such as 4+2=6.  Then they will cut and paste objects to reflect the equation they wrote, using written + and = signs as demonstrated by the teacher.

                                                                       ****  +  **  =  ******

                                                                       4    +   2   =       6

Second example:

To help third or fourth graders (or older students with weak math skills)

My objective here was to help students with poorly developed number concepts, such as with multiplication.  I have found that most students who do not do well in multiplication, that it is sheer torture for them to memorize the “tables”, have a problem in common. They simply do not understand that multiplication is a shorter way to add. 

1. First, I give pairs of students envelopes in which are 30 small squares of colored construction paper, or similar items to be used to count/add.
2. I work with the students in addition, giving them several repetitious adding problems, such as 5+5+5+5+5 = ?  The pair of students manipulate the squares, so they have five groups of 5 squares each.  They count the squares, and write “25” as their answer.
3. We repeat the activity several times: 3+3+3 =?       4+4+4+4+4+4=4 =?
4. Then I ask the students if they can see what we have been doing…Is there a shorter way to write an equation to demonstrate what we have been doing?
5. Most students come up with the answer, which is: oh….there are 7 fours, so 7 groups of 4 = 28.  The teacher or a student can then demonstrate math “shorthand”: 4 x 7 = 28.
6. We will then continue to demonstrate that the reverse is also true: 7 groups of 4 is also 28….
7. Once the students grasp this idea, and it may take several sessions over several days, they finally truly understand what is multiplication.  With practice using concrete objects and examples, they will find it much easier (because it is more meaningful) to remember the multiplication tables.
8. Follow-up activity:  Another day, and can be used with all primary levels.…Students will need to see that there are many different ways to express numerical value.  If they do not understand this basic concept, it will slow their progress in math processes.
9. Ask a student to write a number on the board…..(a number within the span of math studies of the class).  If he/she write “ 9 “, ask the class, “What other ways are there to show “9”?  At first, they my not understand what you mean, so you may have to demonstrate:  8 + 1 + 9.      or     7 + 2 = 9.
10. Have students express these in drawings: ******** + *  = 9  ******* + **  = 9
11. Then continue with other numbers, other example, using concrete objects, and/or drawings.
12. When students REALLY understand this, they will expand too include various math processes, and have fun:  EXAMPLES: 9 = 3+3+3      9 = 10 – 1     9 = 2+2+2+3       9 = 3 x 3     9 = 100 – 91, etc.

FINAL COMMENTS:

• The activities that I chose, use a wide variety of Multiple Intelligences: linguistic, musical, kinesthetic, interpersonal, spacial/visual, logical- mathematical.
• With Bloom’s Taxonomy, they begin with Knowledge and Comprehension, reach Application level (at which Bloom said, “Real learning begins at this level”), and some go on to Analysis and Synthesis.
• Since research shows that 88% of learners learn BEST visually, 10% auditorally, and 2 % tactilely, but we do NOT know which is prominent in each student, we need to use all 3 methods in all of our activities. The activities I use incorporate all three vehicles for learning: They SEE (the board, the book, a worksheet) , they LISTEN (to the other students, to the tecaher, to a CD of music or a story), and they DO (writing, cutting, coloring, etc.).

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Find more articles by Elaine at The English Corner.