Teaching Mathematics

Session 6

Math Failure

• Students are failing in math as in reading• as compared to other countries throughout

the world• Compared to ourselves over time• As compared to our needs in relation to what

we need to run our economy and workforce

Math Failure

Math Failure

Math Failure

• As you saw from the videos, The united states trails the world in math

• Singapore is a leader• In a recent speech, Bill Gates stated that he

was scared for our countries future we will not have the workforce to compete with other nations

Math Failure

• The strange part is – In fourth and eight grade, US students score above

average in math testing, but by 12th grade we are below average

– Specifically - 23% of fourth grade and 32% of eight grade students perform below basic for their grade level although this is not great, it is improvement since 2003

– However, test for 17 year olds have not shown gain

Math Research

Math does not have the rich full body of research that reading decoding has

However, a great deal of research suggest that proficiency develops out of five intertwining strandsa) conceptual understandingb) procedural fluencyc) strategy competencyd) adaptive reasoninge) productive disposition

Math Research

these five strands can be into three Learning principles

1. Teachers must be aware of a students preconceptions and be willing to activate those preconceptions and link them to knowledge

2. Teachers need to understand that competence in an area requires both conceptual and factual knowledge

3. Teachers need to provide assistance to students in developing the metacognitive strategies that support students in monitoring their learning progress.

Math Research

Meta cognition- learning to learn

Metacognition

Metacognition

Big Ideas

• Un like reading- teaching to Big Ideas is very important in math

• There are a series of concepts that are the foundation to more complex concepts

• Math, the spiral curriculum concepts is very important

Big Ideas

• Some of the basic include – Addition, subtraction, multiplication, division.

• However, there are other foundational concepts that interweave through out learning math, such as place value, , of change, commutative property, identity property, associative property number sense ( base ten and equivalences

Big Ideas

• These big ideas work together• Adding or subtracting something as simple,

30 +9 +7 =30 +(9+7) = 30 + 16= 46

Or- 9 is one away from ten, 1 minus seven is 6, therefore 30 plus ten plus six =46

• You can use, commutative property, base ten number sense

Big Ideas• When using big idea, you need to keep the rules general enough

to apply to many different applications and not too specific that they can only be used just once.

• Think of the rule of volume- – Rectangular prisim-– Wedge– Triangular pyramid– Cylinder– Rectangular– pyramid– Cone– Sphere– cylinder

Big Ideas

• Rather than have a different rule for each of them. Have students see the similarities and differences and come up with generic rules

• Base time height- prism, wedge cylinder• 1/3 times base times height- Pyramids- cone• sphere-= 2/3/base time height

Conspicuous Strategies

• Should lead to the acquisition and utilization of knowledge- so it helps you remember it and use it to solve a problem

• Keep the strategy as simple as possible• Let it apply to as many situation as possible

Conspicuous Strategies

• Link the strategy to prior knowledge• Introduce the strategy• Use a graphic that helps explain it• Model it• Have the students do it with you in a scaffoled

way• Try guided practice

Conspicuous Strategies

• Look at these problems, is there one strategy you could use to solve them all?– Five packages of punch mix makes four gallons , How many gallons

of punch can john make for the party with 15 packages?– How long will it take a train to go 480 miles to Paris if it travels at

120 miles?– What is the average rate of a car that goes 450 miles in 9 hours?– How many pounds is 8 kilograms?– The oil transferred from a storage area has filled 44 tanks. There

are 50 tanks. What precentatge of the tanks are filled?– There are 52 cards in a deck. Thirteen of the are hearts, The rest

are not hearts. If you took a trials until you drew 26 hearts, about how many would you expect to take?

Conspicuous Strategies

– One of the most important parts about learning a strategy, is to have a deep understanding of it

– To gain a deep understanding, you need to be exposed to it, use it in many different types of settings- like the previous examples

Mediated Scaffolding

– Too often no scaffolding is provided during math instruction

– Teachers show it once or twice and then students practice it

– Often the students practice it, by not doing it correctly, and they practice it that way and learn the wrong way, the teacher does not notice they are doing it wrong

– Provide scaffolding , limit what mistakes they can make.

Mediated Scaffolding

– An important part of scaffolding is to activate prior knowledge

– And to be aware of what prerequisite skill is necessary to learn the skills

– Case example

Strategic Integration

• Students must not only know how to use strategy, but must know when to apply the strategy

• Students must know how it is related to other concepts

• Must know when to apply them

Review

• Review is most important with math.• POD is a great method• Homework- great method• Drill and practice gets a bad wrap• Uses assessments to determine what needs to

be reviewed-• Students learn things for the test, but cannot

apply it later during different situations

Selecting Tools

• Check out the reading level and the vocabulary

• What is the extent of the scaffolding provided- best if you do not have to create it yourself

• How is it related to prior knowledge

Activity

• Read the article,• Then discuss in your group, the following:

Someone will need to report out on your discussions.– is this the practice that is followed in your school?– Do you agree with this practice?– What do you find objectionable– What do you agree with