Large scale MTE studies

Audio Transcript Auto-generated

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  As I said, this the t d. Sorry the Mt.

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  21 was then followed up by the

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  teacher Education Development Studies in mathematics,

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  um,

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  or T d s m for short. This is the largest scale study.

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  Um,

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  and

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  some of the, uh they had a lot more questions,

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  so But they asked questions also on a policy and institutional level to ask What?

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  What would character size programmes that lead to high content knowledge and P C.

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  K in mathematics?

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  Um and

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  so there was a strong focus on on the knowledge itself as an outcome.

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  They also looked into what the relationship is

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  between beliefs and of the teacher educators.

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  And those are the future teachers. I'm not gonna touch on that.

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  And they tried to also find out something

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  about what were useful practical or school experience.

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  Um organisations What were most effective?

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  Some of these things I feel were answered more than others.

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  What method?

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  Well, there were 17 countries involved,

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  and this time it was survey data from more than 15,000 primary and

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  more than 9000 lower secondary future teachers.

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  And they also ask close to 5000 teacher educators this

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  time it was 500 institutions of pre service teacher education,

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  451 part, so it could be several units within an institution.

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  451 units were preparing primary teachers and 339 secondary teachers.

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  They looked into opportunities to learn belief knowledge,

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  just like empty 21 but also national institutional policies, curricula. And

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  yeah, it was really It really is a very large scale study.

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  I don't know why Maria Teresa, who had a lot of this go crazy.

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  Uh,

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  here's an overview of some of the parameters and some

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  of the connexions that they wanted to look into.

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  Um,

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  you can you can look into that more if you're interested.

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  The results?

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  Well, they found that there were there was a complex amalgam,

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  as they say of of factors.

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  Um, so and I'm going to quote here. That's why there's little starter.

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  Remind me from a substantive point of view.

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  We learned right that achievement in different domains of teacher knowledge.

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  So the content, knowledge, the mathematical pedagogical content,

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  knowledge in the general content knowledge can differ a lot

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  and the achievement of teachers from different programmes

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  within a country can do for a lot,

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  too.

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  We can learn the most for policy efforts with

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  within countries to improve the effectiveness of the system.

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  Overall,

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  teacher knowledge does not seem to be an exclusive function of societal features.

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  All the features of incoming students all of the length

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  or the structure or the content of teacher education only,

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  but a complex amalgam of these characteristics.

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  And perhaps that is not surprising that the social context and the culture uh,

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  what the students know when they come in, how long the education is,

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  how it's structured and what is contained in it are all things that influence.

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  But that's basically what what they say here,

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  Um, based on the way that the student teachers performed in the, uh, sorry.

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  Now what they said about the opportunities to learn mathematics, they

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  they tested what number of groupings were gave the best fit,

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  and they came up with three and they've shown here in a graph,

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  you can see the darkest line, the first class one, in a sense,

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  so that's a high level of university mathematics as you can and and on the

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  on the y axis, you have the probability that somebody would take these topics,

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  and you can see that for all but advanced calculus and topology.

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  The students have more than a 50% charge of having

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  had these courses and even things like differential equations,

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  set theory, logic, the foundations of geometry differential geometry.

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  Uh, and I think multiple and cultures can be included there.

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  There's more than 80% chance that students in this group have taken these,

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  even if they were sometimes elective,

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  uh, compared to the lower group, which is much more school mathematics.

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  So number theory here, I don't think means mathematical number theory,

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  but just the fear of number, um, slightly different.

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  Uh, so they've had

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  that reasonably covered and they've done some probability.

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  And the rest of the topics, uh, there's a very low chance that they've taken this.

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  So that's the third class that school mathematics.

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  And in between, that is the class to which is sort of

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  less advanced or more basic university mathematics. So they've taken some topics.

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  Um,

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  there's there's a reasonable chance that they've taken them some statistics, um,

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  some foundations of geometry, But

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  there's very little chance that they take multi calculus in topology, so uh,

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  that was the way that they grouped

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  the opportunities to learn mathematics. And

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  then they could even say that certain countries fell into some of these groups.

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  So Thailand and Malaysia were in the first group.

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  Most of the countries were in the second group,

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  but Germany and Singapore were in the lowest group.

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  And you can be surprised. I'm sure

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  the Germany of all countries would fall into

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  teaching school mathematics only,

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  and that had something to do with which programmes had been selected.

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  So they do make a comment about it

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  that one institution probably alters the overall picture.

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  They did the same for P. C. K for mathematics,

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  and um, also came up with three classes there.

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  And you can you can sort of get the picture that

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  it was another very broad mathematics pedagogy on my PC.

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  K.

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  It was what they called functional or it was a focus just in teaching methods.

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  So those are the three groups they have here,

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  so either you cover a lot or you cover

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  few topics to a high degree.

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  But certain things there's a there's less chance that you cover those,

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  such as the foundation of mathematics or philosophy of mathematics

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  or context conditions, um, or even effective

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  issues. So

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  but and then you can see the last group cover.

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  Teaching methods cover something about development of mathematical ability,

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  but not a lot of observations.

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  And not a lot of the more advanced topics and PC.

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  So those are the groups. Um, you might

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  I don't know what would surprise. You're not, uh, again.

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  We had Germany mostly on teaching methods on the lower group.

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  Um, there were three countries in the middle group Taiwan, Singapore, in Poland,

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  and then Botswana, Malaysia and the Philippines, Switzerland, Thailand,

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  Russia and chill.

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  I had a broad curriculum.

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  There were four countries that were hard to place,

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  and the way I understand it is because they were too much variation within

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  the countries as you couldn't really say that they had a very unique profile.

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  I have been a little bit naughty nonetheless and

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  and put them in a little

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  table based on

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  what they seem to lean the most towards.

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  And we get this picture that in Thailand and Malaysia, we have

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  at grant student

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  university, mathematics and a broad range of mathematics. Um,

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  B C, k, uh, concepts or coverage.

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  We have, uh, Russia, Philippines, Chilli, Botswana, Switzerland and,

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  to some extent,

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  the US and Norway with more basic university mathematics but very port

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  P C K.

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  And a little bit less broad, more functional. PC k.

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  We have Taiwan, Poland and possibly Georgia,

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  um, and

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  Spain sort of

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  teaching methods but mathematics.

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  And then when it comes to school mathematics,

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  you might find it very interesting that Singapore is there, that they spend a lot of,

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  uh,

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  that the content that teaches mostly school mathematics and that the

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  P C K is not covering all of the aspect.

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  And I think it's, uh

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  it's interesting to look at the culture and the way

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  one understands the job of the teacher in these countries.

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  Um, and we can talk about that. And then Germany again placed place there. And

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  yeah, maybe that's why the Germans continued looking into this. I don't know. Um,

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  so that's an interesting thing.

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  Um, they then also, of course, uh,

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  looked at Well, maybe I should say that it was quite surprising

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  that there was a difference between

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  the future. Uh, if you saw in the performance on the tests

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  that

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  teachers that had done a functional curriculum actually had better P c k scores.

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  So maybe I should just go back to this table.

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  Uh,

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  so and I think this raises a very interesting

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  point that we discussed in a workshop last week.

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  If you try to cover all the PCs that we're talking about,

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  the broad mathematics pedagogy here, uh,

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  they were actually the students that had worked in a functional curriculum,

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  which then would be mostly Taiwan and Poland,

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  but possibly also institutions elsewhere.

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  They performed

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  a little bit better. There was a difference in 4.2 test points. So not super much,

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  Um, then those with a broad curriculum.

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  And then they those who had just had the teaching methods,

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  P C K curriculum performed worst of all.

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  But of course, it's hard to say.

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  Does this have to do with the test questions or is it really?

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  Because it's better to learn a lot about fewer things? So,

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  um,

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  they conclude that

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  primary teacher education, which we're talking about here, maybe,

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  but less pronounced, maybe less different, less, uh,

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  genius than than previously assumed,

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  because there are some topics that's taken by most teachers.

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  But they also feel that the culturally shaped visions

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  of what eternal should be existing country levels,

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  as well as

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  within countries where you might implement different versions of the divisions

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  and then they end up with,

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  Well, they don't end up with. But in the overarching results,

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  they come to that figure that I had before the summarises some of the factors.

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  I don't know why it copied so badly.

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  But, uh, so, interestingly here the gender was found to be

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  a factor.

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  The boys perform better or the young men perform better on the content knowledge,

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  but not the P C. K.

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  And this could be something to do with the history of the whole school system.

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  The way they perceived that they had done in high school Influenced, uh,

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  was correlated to both their content knowledge and their PC K test results.

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  The number of math classes they had taken to both and their

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  motivation both for the subject and more extensively also to both.

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  The opportunities to learn mathematics influence both of these.

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  But they found more indirect link where it appeared to be something about that

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  teachers that had high school achievements, that we're good.

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  We're more likely to pick, uh,

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  programmes that had more opportunities to learn mathematics pedagogy.

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  So that was a bit interesting.

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  Um,

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  so gender,

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  high school achievement and a number of mathematics courses were

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  the most highly significant when it came to content,

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  knowledge and high school achievement and a number

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  of math courses most highly significant for P.

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  C. K.

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  And that could be a surprise that it's not

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  the number of PC care courses and and motivational,

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  of course.

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  Um so it's interesting that the content courses during

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  teacher education influences P C K so strongly,

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  while the P C K courses matter less.

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  These factors were fairly strong,

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  so whether or not the courses were research based didn't seem to matter so much.

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  And, um,

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  as I said, some of this could be explained by the students.

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  With better high school,

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  the team tend to choose courses that has

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  more opportunity to learn both mathematics and PC.

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  I'm gonna continue this in a third recording,

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  so hang in there