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What I Think A Good Math Teacher Is:
Math Portfolio
Gina Keesee
I think a good math teacher is someone who can engage their students in true problem solving; require their students to use prior knowledge learned, in a new situation. My cooperating teacher is very good at doing this, so I have learned a lot from her. In presenting the problems that I taught to my class, I really tried to make the problem an extension of what they were already learning, only harder. I really wanted them to use their problem solving skills. I presented the problem, the majority of the students solved the problem, and then I would collect their papers for evaluation. It was eye opening to see who still had not grasped a concept that they had been working on for over a week; I was also intrigued by some of their thought processes and different ways students came up with to solve the same problem. For those that needed accommodation, they were given a few more minutes, or paired up with a classmate that could help them. If someone finished first, I would have them start working on another similar problem.
A good math teacher needs to be comfortable in front of her class and they need to take the time to make their lessons are as fun and engaging as possible, and interdisciplinary if possible. A good math teacher should be assessing all the time, using formative assessment, mental notes, and summative assessment with tests, quizzes and projects. This assessment should serve as a guide for a good math teacher to know if they can move on with their lesson, or they need to revisit a concept. Good math teachers know how to differentiate their curriculum to meet the needs of those who are academically advanced, as well as those who are academically challenged. These teachers also know when to accommodate a student. Being a good math teacher also entails being able to incorporate technology when you want to, but not to rely on it; and to use manipulatives when necessary or for fun, to help a student learn a concept such as fractions or multiplication etc.
I have been lucky because in addition to the lesson that I taught, and my three required math problems, I have been in charge of calendar math since the beginning of November. So in addition to doing the calendar and the daily depositor, I have also presented an extra problem for the students to work that I created or found in their math book. These problems have also been extensions of what the students were learning. One day, when I didn’t have a problem ready, we did the Problem of the Day, and this also required the students to use their problem solving skills.
One day, my cooperating teacher had to go to an emergency meeting, leaving me in charge of math. She explained everything that she wanted done, and I had a helper in the room too, but it was very tiring actually having to do everything myself, assess to see if they were getting the concept, help those that weren’t getting it, keep the others on task, and keep order in the classroom. This lesson was about the “nines” multiplication tables, and I taught them three different ways to learn the “nines.” An example of the first way would be: 9 x 3= ? Students would start by using their fingers and doing the trick of putting down their number three finger (middle finger on their left hand), and then counting how many tens were to the left (2), and how many ones were to the right (7), so the answer to 9 x 3 is 27. They also learned that all nines multiplication can be checked by adding the product numbers such as for 27, 2 + 7 =9. The last way I taught them was by grouping (3 groups of 9 is 27). They could also draw a picture to represent this. I wish someone had taught me to use this trick! Although I had a helper and we went over and over it, some students still did not see the light. I tried to proved more accommodation for these students by working one on one with them. They had a workbook page to complete for assessment purposes, so it will be interesting to see who understood this lesson.
Because I have done so much observation and so many math problems with the students, I am feeling more comfortable teaching math. I am very appreciative of having the chance to teach these problems with my class, because I became more aware of what I still need to work on, although I felt that it has gone well overall. I was also able to reflect on the fact that although there was no differentiation needed for this class, I did accommodate quite a few students who needed extra time, as well as extra help from me or the helper. The following is a sample of some of the problems I have taught:
1) Keesee.P3.Gr3.
Topic: Estimate Products: Rounding numbers to estimate products
Heuristic: Draw a number line or a diagram. Round before you multiply.
The milk carton problem:
The head of the cafeteria at Waller Mill orders 285 cartons of milk each day. About how many cartons does she need to order in five days?
Estimate: 5 x 285= ???????
Possible method: First the students would need to understand that “about” means “an estimate or number close to the exact number.” An easier way for them to solve this would be to round 285 up to 300. Students should then solve for 300 x 5= 1, 500. The head of the cafeteria needs to order “about” 1,500 cartons a week.
Greenes, et al. (2005). Chapter 21: Estimate Products. Houghton Mifflin Math, Virgina (pp. 584). Boston: Houghton Mifflin Company.
I chose this problem because they had been working on rounding and I wanted to also assess who understood “about.” I really liked this problem because they had to incorporate more than one problem solving skill and it made them think. This was one of the first ones that I did during calendar math, and I learned that they couldn’t multiply 300 x 5, but that they solved it by adding: 300 + 300 + 300 + 300 + 300 = 1, 500. So I got a better idea of where third graders are with multiplication at the beginning of the year, and I learned to never assume anything.
2) Topic: Problem Solving: Analyze Strategies
Heuristic: Use a pattern to organize your list,
Make a chart
The Venus flytrap problem:
Suppose Jan packed 54 Venus flytraps in boxes that hold 10 plants or 1 plant. How
many different ways could she pack the boxes?
Answer: There are six different ways she could pack the flytraps.
Possible method: Use a pattern to organize your list:
10 boxes / 5 / 4 / 3 / 2 / 1 / 01 box / 4 / 14 / 24 / 34 / 44 / 54
Before you fill in your chart, write down all the ways you can come up to pack the
flytraps.
Now check your answer.
Charles, et al. (1999). Chapter 2: Analyze Strategies: Make an Organized List. Foresman-Wesley MATH (pp. 60). Menlo Park, CA: Foresman-Wesley.
I chose this problem because they had just completed a unit on reading about different plant types, one of which was the venus flytrap, and they had just finished a week or two of learning about how to complete these charts. This was more of an assessment problem for me and my cooperating teacher to see who had really learned how to complete a pattern chart. Once again, their answers were eye opening.
3) Keesee.P7.Gr3.
Topic: Subtracting three digits
Heuristic: Work a simpler problem
Use mental math
The sandwich problem:
At the town picnic, there were 450 sandwiches. By the end of the day, there were only 73 sandwiches left. How many were eaten?
450
- 73
Students need to understand that they can’t subtract three from zero, and they need to regroup, borrowing from the tens, changing the zero to 10 and the five to four, then they need to regroup again because they can’t subtract seven from four. Four becomes fourteen and in the hundreds place, that four becomes a three. So the answer is:
450
- 73
377
Now check your answer: 377
+ 73
450 377 sandwiches were eaten.
Source: Original problem by Gina Keesee
I chose this problem for them because they had just started subtraction and I wanted to see if they would have trouble with three digits. This didn’t present too much of a problem for most of them. I recall about three people having some difficulty and requiring assistance from a peer.
4) One problem that I made up was about someone making cookies and then packaging them in boxes; only six cookies could fit in each box, and there were eight boxes. How many cookies were there all together? They needed to figure out that if eight boxes had six cookies each, there were 48 cookies. I collected their work and most of them drew the eight boxes with six dots in them, and a few actually multiplied 6 x 8. I guess this type of assessment can really help to see who is where, in their concept attainment, and problem solving skills.
5) Keesee.P8.Gr3
Topic: Word Problems
Heuristic: Make a chart
Draw a picture
Work an easier problem
The walk-a-thon problem:
Tilly is doing a walk-a-thon at Waller Mill. For every ½ mile that she walks, she gets .50 cents. When she finished, she had raised $2.50. How far did she walk?
Tilly walked 2 and ½ miles.
Have them add .50 +.50 until they get to $2.50= .50+.50+.50+.50+.50
Instruct them that for every .50 cents, Tilly has walked ½ mile so when added together, she walked 2 and ½ miles. (.50+.50= 1 mile) (.50+.50= 1 mile) and the extra .50= ½ mile
Idea inspired by the website: math.about.com (Third Grade Math Word Problems)
I chose the previous problem because it was a difficult problem and required them to come out of their comfort zone and really use their problem solving skills. It was also a difficult problem for me to explain, so it required me to come out of my comfort zone too and really think about a way to explain it that didn’t sound jumbled and confusing. This problem was one that several of the students did not finish before our time ran out. I may revisit a problem similar to this one at a later day to see if their concept attainment has increased.
The following is the lesson that I taught. I really like this lesson and I learned the idea from a second grade teacher that I substituted for in the past. My cooperating teacher and I discussed my idea and then modified it on several levels. We agreed that it would be more interdisciplinary if we had the students use their full names and then count up how many consonants and vowels there were in their names, and write their own fact family sentences using these numbers. This lesson can also be modified to use with multiplication, division; with fractions and decimals:
Waller Mill Fine Arts Magnet School
3rd grade lesson plan, addition and subtraction fact families.
Gina Keesee
Keesee.LP#2.Gr.3
Title: Fun with addition and subtraction fact families
Context: This lesson is designed for a 3rd grade class at Waller Mill Elementary.
This class has 22 students, and this is a review lesson on addition and
subtraction fact families.
Objective: Students will create their own addition, and subtraction fact family
sentences based on the different letters in their names. Students
will establish a relationship between addition and subtraction.
SOL strand: Number and number sense
Virginia SOL: 3.4 The student will recognize and use the inverse relationships between
addition/subtraction and multiplication/division to complete basic fact
sentences. Students will use these relationships to solve problems such as
5 + 3 = 8 and 8 – 3 = ____.
Materials/ Resources needed: overhead projector, students own pencil and paper, handout with the A-Z going down the left hand column.
Time: one hour
Content and instructional strategy:
1)Review fact families and demonstrate a simple one on the overhead; have them write their own fact family sentences using the numbers 8, 6, 14. Tell the students they are going to create their own fact family sentences using the different letters in their names.
2)Demonstrate how to create a fact family by using my own name: Gina Hall Keesee. Use the overhead projector and the handout with A-Z written down the side; show the students how to make tally marks for how times they have a letter in their name. Demonstrate that for the letter “A,” I would have 2 tally marks beside it and for the letter “B,” none, but for “G” I would have 1 tally mark etc. Give them 10 minutes to complete this, walking around the room, guiding where necessary.
3)Next demonstrate my own fact family sentences: I have 14 letters total in my name, 7 consonants and 7 vowels, so mine is easier to do: 7 + 7= 14, 14-7=7 etc.
4)Have the students use consonants and vowels first, and then allow them to create another set using whatever definition they want and that works with their numbers.
5)Practice: Select random students to come up to the board and write the fact families they created with consonants and vowels, telling the class how many of each are in their name and how many letters they have total in their names. Next call on different random students to come up to the board and write the fact families that they have created with their own definitions.
6)Students will help the teacher create fact family sentences using the number of consonants and vowels from the entire class. First, the teacher will tally the number of each letter using all the students’ information, then add up all the tally marks; add up the consonants and add up the vowels. The teacher will demonstrate all of this on the overhead, while having the students take notes in their math journals.
7)The teacher will lead a whole discussion, asking what the students learned about coming up with other ways to create addition and subtraction problems. Have students brain storm other ways to create fact family sentences.
8)Sample summary questions
a)how did you make sure that you had the correct number of tally marks for number of letters in your name?
b)Was it difficult to find three numbers that worked together to make a fact family sentence using the consonants and vowels in your name?
c)Was it more difficult than you thought to create your own definition for what you would use to create your own original fact family? What was the most important thing you learned today?
Evaluation: Exit card
Same directions apply as to practice but have students go home and use a family members’ name. Bring back to school and discuss in math class.
Differentiation and Adaptation: If there are ELL students in the class, have them partner with another student in the classroom for extra help. Also, if there are any students that may have, dysgraphia or dyslexia, they may use a calculator and may need assistance from the teacher to make sure they can read the problem, so they aren’t transposing numbers. The amount of practice can be determined based on the needs of the students.
Resource: Gina Keesee
Observation of CT’s lesson about fact families to be familiar with what they are. The lesson plan idea is mine.
This lesson plan would have been more fun and engaging if I had time to write fact families using the information from the entire class. There isn’t much I would change about it except not having the students use their middle names, this was too confusing for some of them. Once again, I learned not to assume so much. I expect a lot out of them and sometimes I forget that they are only eight. My teacher took the opportunity to piggy back off me and go right into teaching them how to write division and multiplication fact families with their information. Upon reflection, it is daunting to think that I will have to conduct these lessons by myself; this lesson was tiring even with my cooperating teacher and the helper both in the room.
Good math teachers should be able to make math interdisciplinary by using books such as picture books, to create other engaging and fun math lessons. I really liked writing my literature connections because I was able to choose the books that I wanted and justify why I thought they would be great to use for a math activity. This activity forced me to be creative, and now I have a lot of ideas about how to connect literature to math whereas I hadn’t really thought about this concept before. The following is my literature connections that were submitted:
Literature Connections
The Pampered Chef: Kids in the Kitchen
Description of contents:
Kids in the Kitchen is a cookbook designed for children of all ages. It contains over three hundred recipes that young chefs can choose from that requires them to measure, pour and convert. It is divided into ten sections that list the ingredients and tools that will be necessary for each recipe.