FACULTY OF EDUCATION AND LANGUAGES
HBMT 2103: TEACHING MATEMATICS IN YEAR TWO
NAME : TIONG MEE CHING
TUTOR NAME : MR. ANDY JANANG AK HENRY TAWIE
TUTOR NAME : MR. ANDY JANANG AK HENRY TAWIE
Sunday, November 21, 2010
Intro: Misconception In Elementary Mathemathics
§ INTRODUCTION:
MISCONCEPTIONS IN ELEMENTARY MATHEMATICS
The most common math misconceptions are addressed and strategies are provided for helping elementary students eliminate these tightly held mistaken beliefs. Just like in other subjects, students have misconceptions in mathematics. These misconceptions are derived from their prior knowledge and experiences with numbers in their everyday lives. These misconceptions hinder the learning process, because they are tightly held by students. Their teachers need to provide tangible experiences to break these misconceptions.
Eliminating mathematic misconceptions is difficult and merely repeating a lesson or extra practice will not help. Telling students were they are mistaken will not work either. Recognizing student misconceptions and immediately focusing a discussion on the misconception is important. Providing guiding questions using inductive reasoning is the best approach.
This also approach to misconception on capacity may arise among the students while teaching Volume of liquid especially when comparing capacity of two containers that can hold more. Students often make the comparison on height rather than its capacity which the tallest container always has greatest volume. This a misconception caused by visual perception. Also they learn this from eating in fast food restaurants and similar locations that display cup sizes. The tallest cup always holds more, because of the way they are displayed.
The best way to eliminate this problem is to have students fill tall containers with water and then pour the water into a shorter container which has the same volume. This is a difficult misconception to break and even adults have issues with this misconception. The most effective method of eliminating math misconceptions is to address them immediately when observed. This imperative, so students do not carry these misconceptions any further and develop a better understanding of mathematics especially involves visually comparison.
Video: Measuring Liquid Volume In Non-Standard Units
One of the methods to measure Volume of Liquid is by using a graduated cylinder. It's been shown on above video clips.
Two reasons why I choose this video are:
- animated which can attract young children to learn it.
- clearly shows the actual way to read measurement on proper units.
Method: Measuring Liquid Volume By Containers
§ METHOD:
MEASURING LIQUID VOLUME BY CONTAINERS
What’s makes difference between volume of solid and volume of liquid? Solids have defined shapes either regular or irregular. If the shape of a solid is regular, then its volume is calculated by geometrical means and if not, it can be figured out indirectly. In any case, the volume is defined in fixed directions.
However, liquids have no definite shape in which occupy the available space of a container. They spread over the entire the area of section and stands up to a height. Hence the volume of a liquid is the volume of its container up to the height of the liquid level. For this reason, the volumes of hollow shapes are called as ‘capacity’ of the shape. This concept is mainly used in measuring volume of liquid.
One of the methods to measure Volume of Liquid is by using a graduated cylinder (Figure I). It can be used to know the volume of an available liquid. As mentioned earlier, the liquid volume is directly proportional to the height of its container of uniform cross section. Therefore, in a graduated cylinder, the readings are calibrated to directly give the value of the volume.
Figure I: Measuring volume of liquid by graduated cylinder.
Materials for Teaching Aids (I)
The First Teaching Aids I created more to read and measure the capacity volume of liquid. The purpose to ensure students knows how to measure in proper metric units such as milliliters (ml) and liters (l). To let students expose to standard units before to non-standard units. With these practical works to students, it would let students bear this knowledge in mind as long term memory.
TEACHING AID (I):
§ Measuring cup
§ 4 glasses of equal size
§ Water (Coloured)
Teaching Activities For Teaching aids (I) - High Achiever Students
TEACHING ACTIVITIES FOR:-
TEACHING AID (I)
HIGH ACHIEVER STUDENTS
TITLE – UP UP.. IT GO.
In this lesson, students recognize and use the attributes of volume. They engage in activities that promote understanding of how to measure and compare volume using non standard units. | |
LEARNING OBJECTIVES | |
Students will:
|
MATERIALS:
--- Measuring cup
--- Guessing worksheet
--- 4 glasses of equal size
--- Water (Coloured)
--- Measuring cup
--- Guessing worksheet
--- 4 glasses of equal size
--- Water (Coloured)
ACTIVITIES:
> Divide students in group of three or four.
> Ask students pour water at different levels such as
a) 1/2 cup,
b) 1/3 cup,
c) 3/4 cup and
d) 1 cup into each glass.
> Put the glasses next to each other.
> Ask students fill in the guessing paper.
QUESTIONS AND EXPLORATION IN GUESSING WORKSHEET:
> Ask the students these questions:
> Which glass has the most water?
> Which glass has the least amount of water?
> Which measurement is the most? 1/3, 1/2 1/4 or 1 cup???
> Which is the least??
ESTIMATION:
How many glasses of the 1/2 cups would it take to equal 2 cups?
How many of the 1/4 cups do you think it would take to equal 1 cup?
EXTENSION ACTIVITY (RECOMMEND WHEN HAVE EXTRA TIME):
As the children get better at estimating use different substances such as rice, popcorn or butter. Also you can have the students put them in order from greatest to least amount or least to greatest amount.
As the children get better at estimating use different substances such as rice, popcorn or butter. Also you can have the students put them in order from greatest to least amount or least to greatest amount.
CONCLUSION:
For this activities pupil will bear in mind that the volume of liquid will be determined based on the height of water. The higher height capacity volume of water in same size containers the bigger quantities of water fill in.
For this activities pupil will bear in mind that the volume of liquid will be determined based on the height of water. The higher height capacity volume of water in same size containers the bigger quantities of water fill in.
Teaching Activities For Teaching aids (I) - Low Achiever Students
TEACHING ACTIVITIES FOR:-
TEACHING AID (I)
LOW ACHIEVER STUDENTS
TITLE – GUESS WHAT?!.
In this lesson, students recognize and use the attributes of volume. They engage in activities that promote understanding of how to measure and compare volume using non standard units. | |
LEARNING OBJECTIVES | |
Students will:
|
MATERIALS:
--- Measuring cup
--- Guessing worksheet
--- 4 glasses of equal size
--- Water (Coloured)
--- Measuring cup
--- Guessing worksheet
--- 4 glasses of equal size
--- Water (Coloured)
ACTIVITIES:
1. Divide students in group of five.
2.Ask students pour water at different levels such as
a) 1/2 cup,
b) 1/3 cup,
c) 3/4 cup and
d) 1 cup into each glass.
3.Put the glasses next to each other.
4.Ask Questions verbally to students by group.
5.Ask students note down the exploration had made on Guessing Worksheet.
GUESSING WORKSHEET (QUESTIONS AND EXPLORATION):
> Ask the students these questions:
> Which glass has the most water?
> Which glass has the least amount of water?
> Which measurement is the most? 1/3, 1/2, 1/4 or 1 cup???
> Which is the least??
ESTIMATION QUESTIONS:
> How many glasses of the 1/2 cups would it take to equal 2 cups?
> How many of the 1/4 cups do you think it would take to equal 1 cup?
> Ask the students these questions:
> Which glass has the most water?
> Which glass has the least amount of water?
> Which measurement is the most? 1/3, 1/2, 1/4 or 1 cup???
> Which is the least??
ESTIMATION QUESTIONS:
> How many glasses of the 1/2 cups would it take to equal 2 cups?
> How many of the 1/4 cups do you think it would take to equal 1 cup?
CONCLUSION:
For this activities pupil will bear in mind that the volume of liquid will be determined based on the height of water. The higher height capacity volume of water in same size containers the bigger quantities of water fill in.
For this activities pupil will bear in mind that the volume of liquid will be determined based on the height of water. The higher height capacity volume of water in same size containers the bigger quantities of water fill in.
Materials for Teaching Aids (II)
My second Teaching Aids will involve students hands-on and mind on activity. This activity would allow students have a chance to measure and to read measurement by their own. Indirectly, the knowledge learn will implement in their mind in long term memory rather than short-term memory.
TEACHING AID (II):
§ 2 cups measuring cup
§ A tape measure
§ A graduated cylinder (500ml)
§ Water Mineral
§ A box of instant pudding for each group
§ 2 cups of skim or soy milk or chocolate milk
Teaching Activities For Teaching aids (II) - High Achiever Students
TEACHING ACTIVITIES FOR:-
TEACHING AID (II)
HIGH ACHIEVER STUDENTS
TITLE – LET’s Be MATH ‘n” CHEF
In this lesson, students recognize and use the attributes of volume. They engage in activities that promote understanding of how to measure and compare volume using standard units. | |
LEARNING OBJECTIVES | |
Students will:
|
MATERIALS:
2 cups measuring cup
A tape measure
A graduated cylinder (500ml)
Water
A box of instant pudding for each group
2 cups of skim or soy milk
IMPORTANT NOTE:
- Make note of any food allergies students may have.
- If cow milk allergies are a concern, then use soy milk instead.
- Floor and furniture protection may be necessary or you can take the lesson outdoors.
ACTIVITIES:
PART I: Math Logic
¢ Review with the students the S.I units to measure volume of liquid.
¢ Divide students in group of two.
¢ Asks students to compare the measuring cup to the graduated cylinder.
¢ Asks them to notice if there are any differences
¢ Fill the measuring cup with water to the rim of the cup.
¢ Note the location of the 2 cup mark on the measuring cup.
¢ Compare the level of water in the measuring cup to the 2 cup mark. Is there a difference?
¢ Next pour the water from the measuring cup into the graduated cylinder.
¢ Observe the results.
¢ Have the students write a constructed response detailing observed and conclusions by draw the demonstration.
PART ONE DISCUSSION TOPICS:
- Is the volume of the 2 cup measuring cup equal to 2 cups? Why or why not.
- How does a graduated cylinder differ from a measuring cup? Is one more accurate than the other? Why?
CONCLUSION PART I:
- This will give the students a good visual as to what the measurement looks like.
- It’s also let students knows that even in different shape and height, the capacity volume of liquid carried still same.
- At the end, students would know that not always the tallest container can hold more capacity volume of liquid.
PART II: Chef Math Cook.
1.Divide students in group of two.
2.Measure out the equivalent of 2 cups of milk in the graduated cylinder.
3.Mix the pudding according to directions.
4..It will be soft set in about 5 minutes.
5.Put into small paper cups or you can put it into ice cream cones.
PART TWO DISCUSSION TOPICS
- Do you enjoy?
- Can you read the measurement on graduated cylinder accurately? If not, why?
- Is the volume of the 2 cup measuring cup equal to 2 cups? Why or why not.
CONCLUSION PART II:
- Students enjoy in this lesson.
- With practical work, students able keep this knowledge as long term memory.
- Students can measure correctly by using graduated cylinder.
Teaching Activities For Teaching aids (II) - Low Achiever Students
TEACHING ACTIVITIES FOR:-
TEACHING AID (II)
Ø LOW ACHIEVER STUDENTS
TITLE – MaTH-CheF COok.
In this lesson, students recognize and use the attributes of volume. They engage in activities that promote understanding of how to measure and compare volume using standard units. | |
LEARNING OBJECTIVES: | |
Students will:
|
MATERIALS:
> 2 cups measuring cup
> A tape measure
> A graduated cylinder (500ml)
> Water
> A box of instant pudding for each group
> 2 cups of skim or soy milk
IMPORTANT NOTE:
- Make note of any food allergies students may have.
- If cow milk allergies are a concern, then use soy milk instead.
- Floor and furniture protection may be necessary or you can take the lesson outdoors.
ACTIVITIES:
1. Review with the students the S.I units to measure volume of liquid.
2. Divide students in group of four.
3. Asks students to compare the measuring cup to the graduated cylinder.
4. Fill the measuring cup with water to the rim of the cup.
5. Note the location of the 2 cup mark on the measuring cup.
6. Compare the level of water in the measuring cup to the 2 cup mark. Is there a difference?
7. Next pour the water from the measuring cup into the graduated cylinder.
8. Observe the results.
9. Measure out the equivalent of 2 cups of milk in the graduated cylinder.
10. Mix the pudding according to directions.
11. It will be soft set in about 5 minutes.
12. .Put into small paper cups or you can put it into ice cream cones.
DISCUSSION TOPICS:
- Is the volume of the 2 cup measuring cup equal to 2 cups? Why or why not.
- Can you read the measurement on graduated cylinder accurately? If not, why?
- How does a graduated cylinder differ from a measuring cup? Is one more accurate than the other? Why?
CONCLUSION:
- This will give the students a good visual as to what the measurement looks like.
- It’s also let students knows that even in different shape and height, the capacity volume of liquid carried still same.
- At the end, students would know that not always the tallest container can hold more capacity volume of liquid.
My Conclusion..
SUMMARY
We know our students learn in many different ways: visual, auditory, tactile, kinesthetic, and social. Most of teachers teach the way they feel most comfortable, and that's not necessarily the way students learn. It's a missed opportunity if teacher don't use the way that a child learns best to hook them and get them excited about learning.
Hands-on practical works obviously engage kids who are tactile or kinesthetic learners, who need movement to learn best. Be found that, hands-on activities let students become teachers especially when students explain and demonstrate skills to each and this make they are validating their understanding of the material being learned and, helping their peers to build and master new skills.
Hands-on activities learning of volume of liquid also lend themselves to authentic assessment and observation, where students follow directions and use fine motor skills during center time. Hand-on activity is specially suit with students has fear of learning mathematics-subtraction. The fear is link with weak in gaining imaginary process concept, then, the most relative way to help students’ is by gaining their confident uses hands-on activities all day, every day. This will help teacher nurture students’ interest to mathematics slowly and will increase.
Indirectly, the learning of volume of liquid begins with concrete (hands-on minds-on activity) experience in realistic situations through measuring the capacity of liquid. standard units, which are measured in millimitres(ml) and litres(l) in the metric system. Meanwhile, non-standard units measured using various containers by stated the capacity wheather more or less. Materials from non-standard units are easier to obtain. It is good to give children experience with unfamiliar systems of measurement . With the hope, after students goes through these teaching activities, they would not be influence by the height of containers to state which one can hold bigger volume (shown on Video 2).
Video 2: Piaget's - Stage 3, Concrete Reversibility.
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