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

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MSPnet Academy Discussion
January 22 - February 5, 2013

Heather Hill, Associate Professor, Harvard Graduate School of Education

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.

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Welcome to Discussion

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

Welcome to the MSPnet Academy discussion, "The multi-dimensional nature of mathematics instructional quality: A first look at teacher and teaching elements that contribute to student outcomes", presented by Heather Hill.

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

So these seemed to be big issues still floating around at the end:

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


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

Dear Heather,
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


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

Dear Dick,

The instrument is described at There's also associated training, if you are interested in getting into the nuts and bolts of the instrument.


Concerns about MQI as illustrated by fractions

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

Dear Heather,

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

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.


Fraction subtraction in TIMSS

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

I wonder if the following problem or ones like it would be picked up by the
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

D 4 - 3

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.