Large scale MTE studies

Audio Transcript Auto-generated

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  good evening. At least on this side of the world. Um,

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  I have taken on an impossible task, namely to summarise, um,

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  some large scale international studies on mathematics teacher education.

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  Um, I will do that in four bits.

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  I'll first introduced the concept of opportunities to learn.

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  Then I go into the first, um, of the studies, the m T 21

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  then move onto the most well known T d S m

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  the teacher education and development studies in mathematics.

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  And then there was a follow up study to that done in Germany,

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  And that will be the last bit that time,

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  um,

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  go into

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  so opportunities to learn is a concept that is very much

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  based on the idea that if we give learners equal conditions,

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  they will have equal opportunity to learn, um, from from where they are.

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  And originally, the concept was seen just as being about content coverage,

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  what was covered, Um,

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  and it then moved on to also include how much time learners were given to learn,

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  because obviously you can have the same content.

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  But if you're not given the same time, it's not the same opportunity

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  over time.

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  It was expanded to take into consideration the cognitive level of the content,

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  the curricula coherence, um, how connected it is and the pacing of the teaching.

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  So how quickly it moves through the content and to some extent, also,

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  whether or not the pacing is adjusted to the needs of the learners.

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  Um, or if you want us to keep pace

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  So that's O T. O.

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  Um,

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  how does one measure something like opportunities to learn?

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  Well, there have been three standard ways.

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  The one is observations in the classroom to see what goes on there.

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  The other is to look at learners, notebooks,

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  what sort of notes they've taken to indicate what has been covered.

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  And the third is to actually ask, Um, that's obviously more easily done with adults.

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  But that is what was done in these in these, um,

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  in the first two of these international studies that

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  I will go through, um, in the rest of this video.

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  So I'm going to move on to mathematics teaching in the 21st century. Mt. 21

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  um, and

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  Mt.

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  21 was in a way inspired by that

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  the Tim studied Third International mathematics science.

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  Um,

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  study mathematics and science study from 1995 showed that

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  different content was actually taught in different countries.

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  So that

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  learners, um,

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  that countries where learners performed high and teams had different

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  mathematical content and learners where they performed less well,

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  So,

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  um, that was the idea that

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  drove this.

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  It was funded by the American National

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  Science Foundation and involved the countries Bulgaria,

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  Germany, Mexico, South Korea, Taiwan and U.

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  S A.

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  You can see the spread of, uh, context there.

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  The primary goal was to examine how middle school

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  what we call sometimes called lower secondary mathematics.

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  Teachers were prepared in these six countries.

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  Um, and the unmistakable conclusion was the teacher education matters.

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  It was even the title of the book

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  that came out, edited by William Smith Secret Blooming

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  or, uh, and Maria Teresa to to,

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  um,

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  it was called teacher Education matters.

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  How do they do this? What was the method?

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  While it was a survey of 2600 student teachers,

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  more or less from 34 different institutions,

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  and they sampled the institutionally also,

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  you sample institutions in the country,

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  and then you ask all the student teachers in that institution they were asked,

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  uh, content questions So more or less a math test, Um, but also P c K test.

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  They were asked about their beliefs about teaching mathematics,

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  and they were asked about what opportunities to learn they have encountered.

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  And the opportunities to learn with both opportunities were for things,

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  opportunity to learn, formal mathematics, opportunities to learn

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  mathematics, Pentagon

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  general pedagogy and then how, what? The opportunities to

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  be out in a practise practical school related experience.

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  What, this way,

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  Um,

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  it's It's quite interesting that in this study they very much, uh,

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  took into account the broader context.

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  So not only did they look into how much time

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  do you have for math lessons in different countries,

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  which, which will say a lot about what the opportunity to learn for the learners are,

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  but also about the work of teachers.

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  Obviously, if you have to have to our lessons,

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  it's very different from if you have 30 minute lessons,

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  um,

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  in many ways,

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  but also how many classes the teacher has to teach.

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  So in Taiwan, a teacher will teach 17.

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  Now I look very hard to see was this per week, which I would assume,

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  but it actually never said so Let's just assume it's per week.

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  So in Taiwan, a math teacher teaches 17 lessons per week.

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  So that means that if you have a 40 hour work with you and and it's, uh,

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  probably more in Taiwan, but nonetheless, if you have a 40 hour work week,

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  you spend less of that less than half of that time, uh, in contact with your learners.

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  Whereas in Mexico you have 40 hours in class.

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  Um, so that, of course, means a lot to what you can cover. And, um,

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  what you, uh, help prepared you can be. So they found a lot of differences in, um,

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  what

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  middle grade topics were taught in the teacher education?

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  Um, whether they were taught common in decimal fractions, exponents, roots,

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  patterns, relations functions.

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  Um, and they also found differences in whether the,

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  um,

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  the student teachers first would have become

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  finished, finished the mathematics studies and then do the, uh,

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  education component so that it was,

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  um

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  um,

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  consecutive because the programme would be consecutive

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  or if it was an integrated programme.

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  So those are also differences and we see that in in the

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  latest studies as well but I'm not gonna go into it later.

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  The opportunities to learn that they saw in

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  the actual teacher education programme also varied,

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  Uh, from student teachers having a total of 1700

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  contact hours to having more than double that. So

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  also, big differences there.

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  Um but,

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  um,

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  what is interesting is that even though

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  there are vast differences within countries,

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  it was still possible to do some degree of country clustering.

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  The mathematics content varied greatly from

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  being nothing in, uh,

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  Mexico of the of the teacher education curriculum to being 60% in Bulgaria.

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  So I listed them here in order Mexico, US, Germany, South Korea time, Bulgaria,

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  um, South Korea and Taiwan taught calculus and linear algebra,

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  and many of the students also took analysis differential equations,

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  abstract algebra to quality and differential geometry.

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  And obviously, in Mexico, they didn't do any of this.

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  So huge differences in how much mathematics were covered.

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  P C K varied less both in time and content.

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  But there were still significant differences.

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  And as you might remember, when I said the methods they used,

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  uh,

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  they had they also tested the PC case course and

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  you can question whether or not that's reasonable or not.

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  That's another storey. But they did so and found that,

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  um, if you had had less mathematics content in your teacher education,

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  your P T K scores were also at least this is a recurrent finding.

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  I would say

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  that the mathematics, um, is a

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  importance to you Can't You can't have strong p c k without having

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  a reasonable level of mathematics.

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  Um, that doesn't mean that you can go with just the mathematical knowledge.

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  Um, they also looked at how much pedagogy did they have?

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  And, uh, in this case, they considered the teaching practise to be part of pedagogy

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  in the Swedish context.

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  We wouldn't do that because we think that you have

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  the opportunities to learn at least P c k.

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  But also some mathematics when you're out in schools. But

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  but that's the way they did it in in, uh

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  in in teaching mathematics for the 21st

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  century and the amount of pedagogy buried from

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  being 5% of the curriculum in Bulgaria to being 75% of the curriculum in Mexico.

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  Despite these huge differences in what was covered in the programmes,

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  the beliefs that the students held about good, uh, mathematics,

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  teaching and about mathematics.

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  Learning

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  had a lot of commonalities,

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  so that's quite interesting.

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  Planning was taken not as a P.

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  C K content, um,

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  as we would probably have done and as Marlon

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  certainly is doing but as part of general pedagogy,

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  and they specifically looked at lesson planning,

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  and what's interesting here is, um,

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  you might wonder why we're the only 2220 for that answered the sex of planning.

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  And that's because when you have these large

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  scale studies and you have a million questions that

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  everybody must answer,

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  then you sometimes choose to or you you often choose to

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  just give some of the respondents some of the questions,

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  um,

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  so that not everyone answers everything,

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  but it still allows you to see correlations.

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  So that's probably what happened here. They

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  I think what happened was that they they were

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  asked to assess a lesson plans and the students

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  were asked to assess a lesson plan and whether they

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  came up with the codes are the codes of preexisting.

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  I actually don't remember but 12 codes, um,

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  and I think they were derived from what the what?

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  The

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  pre service teachers said,

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  um showed up here and then other.

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  If there were a few things they couldn't place but basically 12 codes and Martin,

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  you might want to look at this.

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  Um,

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  they showed, um

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  when you look from different countries,

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  there were big differences and they looked at this in two ways.

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  They looked at which code which

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  students from which country is used, which code and so big differences there.

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  But they also looked into which theoretical terms the student

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  teachers used when they were assessing the lesson plan,

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  Uh, and what they wrote about it. And even there you saw, they saw big differences.

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  So that's quite an interesting finding.

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  And it's also interesting methodological this thing of,

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  of trying to get a sense of what a

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  student teacher has taken with them about a particular topic

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  by looking at what theoretical terms that are using so

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  and

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  hint.

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  Just a very confusing thing in the Mt.

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  21 Report is that they talk about theoretical pedagogy and practical pedagogy,

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  and, um,

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  as you saw, they put the teaching practise under the

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  on the pedagogy.

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  So I'm wondering if that's what it's about, but they never define it properly.

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  But they plot the institutions in a coordinate

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  system based on whether or not they have,

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  how much how much practical pedagogy and

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  how much they're radical pedagogy they cover.

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  And,

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  yeah, I just wanted to mention that they look at that dimension as well as you can see

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  some. In some countries it tends to cluster, but it's not 100%

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  and it's a

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  it's quite spread out,

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  even though there is a tendency that they should have some of both,

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  they're also exceptions.

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  So,

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  um,

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  that was what I wanted to say about mathematics teaching

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  for the 21st century and now to the big one,

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  because this study was then followed up.