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## Topic: "MSPnet Academy: The multi-dimensional nature of mathematics instructional quality"

### Topic Posts

###
MSPnet Academy Discussion
January 22 - February 5, 2013

In this webinar, we will present first results from a study that examines how teacher mathematical knowledge, their mathematics teaching, and other key variables relate to student outcomes. This study features quantitative analyses with a sample of 250 teachers and their students, as as well as more exploratory analyses of teachers with high and low VAM scores. We find that several dimensions of mathematics teaching appear both related to student outcomes and distinct from one another, suggesting that mathematics teaching is multidimensional in nature.

### Archives for this academy

### Welcome to Discussion

posted by: Kimberly Descoteaux on 1/22/2013 12:57 pm

Heather Hill will be posting a discussion topic here after the conclusion of today's webinar.

The webinar will be archived and available to watch starting 1/23/13.

### Discussion Questions

posted by: Heather Hill on 1/22/2013 3:36 pm

1) How can we, as the mathematics education community, take advantage of the coming changes in assessment and teacher evaluation to further implementation of the Common Core standards?

2) How do we support raters (largely principals, but possibly also folks working at third-party assessment firms) to provide accurate feedback on the quality of mathematics instruction?

Also happy to provide more specific information about the study, our rating process, the instruments, and so forth.

*post updated by the author 1/22/2013*

### MQI

posted by: Richard Askey on 1/24/2013 4:17 pm

Where can I read about what you are using for MQI? In the summary on the

power point, I think there are some missing parts.

Dick Askey

### MQI

posted by: Heather Hill on 1/28/2013 12:24 pm

The instrument is described at http://isites.harvard.edu/icb/icb.do?keyword=mqi_training. There's also associated training, if you are interested in getting into the nuts and bolts of the instrument.

Best,

Heather

### Concerns about MQI as illustrated by fractions

posted by: Richard Askey on 1/29/2013 10:07 am

I have now read the brief description and should tell you my

concern. I sent two messages, the second dealing with

fraction subtraction, but with a second meaning of knowing

or not knowing that fractions are numbers. When over 50%

of students answer the question on 1/3 - 1/4 with answers A

or B, the system is broken since one cannot know much if

anything about fractions as numbers and answer A or B. One

could make the same claim about C but my guess is that

most of the answers of C were careless ones. I am not claiming

that all students who picked D know as much as they

should about fraction subtraction, but those who picked A or

B know little. I asked if this type of error would be picked

up by state tests since if it is not, then the framework you

have of favoring multiple approaches but not mentioning

specific approaches will not give an accurate measure of

learning. There was a similar fraction problem in TIMSS-95,

adding three fractions. One answer was what one gets when

adding numerators and dividing by the sum of the

denominators, one was correct, and the other two seemed

to be almost random. Countries split to a large extent

in how they did on this problem. There were some which

had a very high percentage getting it correct and a very

small fraction adding numerators and denominators. As

might be expected, some of the East Asian countries were

in this group, but so was the Flemish part of Belgium. There

was a larger group whose results were not quite as good,

but acceptable. Then there was a gap and below the gap

was another large group of countries. The U.S. was in this

group, below the international average in correct answer

and above this average for the percent adding numerators

and denominators. Until the Common Core, there was

little if any emphasis on fractions as numbers. The

emphasis was on different representations of fractions.

The different representations are not wrong mathematically,

but if the important of fractions as numbers is not stressed

we are likely to continue to get what we have been getting,

which is not adequate. It is possible to improve. Korea

now does much better than it did in 1995, so I suspect

there has been some changes in how fractions are

taught.

Let me mention one common problem students are given.

Is 1/2 greater than 1/3? This is often illustrated by two

answers, one having a large pie and a smaller pie where

1/3 of the larger pie is larger than 1/2 of the smaller. That

is true, but misleading since one should never compare

the size of fractions unless they refer to the same whole.

That is the message which should be learned but is

not taught.

Just teaching material which is "correct mathematically"

is often not enough. One has to know what is vital for

students to learn and make sure this is taught well. I

do not see this as any part of your criteria.

Dick

### Fraction subtraction in TIMSS

posted by: Richard Askey on 1/24/2013 4:23 pm

State tests. This is from the eighth grade TIMSS test.

Item M 02_04

Which shows a correct method for finding 1/3 - 1/4?

A 1 - 1

-----

4 - 3

B 1

-----

4 - 3

C 3 - 4

-----

3*4

D 4 - 3

-----

3*4

Here are some results.

The numbers are percents.

Correct A B C D

Average 37.1 25.4 26.0 9.4 37.1

Korea 86.0 2.7 6.9 4.2 86.0

Singapore 83.1 4.8 5.5 6.5 83.1

Taipai 82.0 2.9 7.7 7.0 82.0

Hong Kong 77.0 4.0 8.7 10.0 77.0

Japan 65.3 15.4 11.1 8.2 65.3

Russia 62.8 12.3 18.8 4.8 62.8

US 29.1 32.5 26.1 10.7 29.1

Finland 16.1 42.3 29.5 8.7 16.1

Canada did not take TIMSS as a country but some provinces did as

did some US states. Here are some of these results

Mass 44.4 21.4 20.8 9.9 44.4

Calif 38.0 28.2 21.6 11.0 38.0

Minn 35.1 23.5 26.3 14.0 35.1

Quebec 33.0 27.3 23.0 13.0 33.0

Ontario 32.5 27.7 22.4 14.0 32.5

Conn 31.3 21.8 25.8 17.7 31.3

Alberta 27.8 34.7 23.7 12.3 27.8

Finland had the highest percent picking answer A. Students who do

that have no idea about fractions as numbers.