Maths transition: Transition Mathematics — UCSMP

Posted on 31 августа, 2023 by alexxlab

Transitions in Mathematics Education | SpringerLink

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Transitions in Mathematics Education

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Authors:

Ghislaine Gueudet
⁰,
Marianna Bosch
¹,
Andrea A. diSessa
²,
Oh Nam Kwon
³,
…
Lieven Verschaffel
⁴

Ghislaine Gueudet
1. CREAD, ESPE Bretagne UBO, Rennes, France
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Marianna Bosch
1. IQS School of Management, Universitat Ramon Llull, Barcelona, Spain
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Andrea A. diSessa
1. Graduate School of Education, University of California, Berkeley, USA
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Oh Nam Kwon
1. Seoul National University, Seoul, Korea (Republic of)
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Lieven Verschaffel
1. Van den Heuvel Instituut -Room nr. 05.71, Katholieke Universiteit Leuven, Leuven, Belgium
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Discusses processes of change and transition across different areas and levels of mathematics education
Provides an overview of the state of research on transitions from both individual and institutional perspective
Describes directions for future research on transitions in mathematics education
Includes supplementary material: sn. pub/extras

Part of the book series: ICME-13 Topical Surveys (ICME13TS)

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About this book
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Bibliographic Information

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Table of contents (1 chapter)

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Front Matter

Pages i-x

PDF
Survey on the State of the Art
- Ghislaine Gueudet
Pages 1-34Open Access

PDF

About this book

This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education.

Keywords

Conceptual Change
Discontinuity
Ethnomathematics
Expert Knowledge
Institutions
Out-of-School Mathematics
Mathematical Knowledge for Teaching
Knowledge in Pieces
learning and instruction

Authors and Affiliations

CREAD, ESPE Bretagne UBO, Rennes, France

Ghislaine Gueudet
IQS School of Management, Universitat Ramon Llull, Barcelona, Spain

Marianna Bosch
Graduate School of Education, University of California, Berkeley, USA

Andrea A. diSessa
Seoul National University, Seoul, Korea (Republic of)

Oh Nam Kwon
Van den Heuvel Instituut -Room nr.

05.71, Katholieke Universiteit Leuven, Leuven, Belgium

Lieven Verschaffel

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Free videos to assist the transition from GCSE to A level Maths

The transition from GCSE to A level Maths can be challenging but, with plenty of practice, it most certainly is a rewarding experience. The chapters below focus on activities which help students to master the key skills that are needed in both AS and A level Mathematics. The topics are mainly those found in the overlap between GCSE and AS mathematics.

Each chapter contains between 10 and 15 videos for students to watch, along with a downloadable PDF of example questions, practice questions and End of chapter exam questions for consolidation.

Please download the Instruction guide for guidance on how to use this resource.

Please note: we have deliberately not included Chapter 8 and somes of the examples, for more information please read our FAQs below .

FAQs

Chapter 8, The Binomial expansion is beyond the crossover content between GCSE and AS level Maths and therefore we haven’t included it. We still want to ensure the chapters align to the Year 1 AS Pure Maths textbook which is why we have retained the numbering of the chapters.

Some examples have been deliberately not included. For example, for Chapter 1, we have Examples 1,3,4,5,7,9,10,11,12,13,14 only.

These correspond to the same example numbers within the chapter of the of the Year 1 AS Pure Maths textbook to allow you to use both resources together.

This resource will help:

to provide stretch and challenge for high achieving GCSE Maths students (aiming for grade 7-9)
students wanting to study A level Maths
students studying AS level Maths
revision for AS and A level Maths students.

Please download the Instruction guide to help you use this resource.

Here are some ideas as to how you may use this resource:

GCSE Students — direct more able students to the resource for some stretch and challenge. The videos explain how to do each example question are a great learning tool.
Year 12 (and post-16) — after teaching a topic, direct students to the resource as a support tool as there are lots of great practice questions and exam questions.
Year 13 (and post-16) — try the examples, practice questions and exam questions after identifying gaps of knowledge and use as a revision tool to consolidate learning.

This resource includes:

Example questions
Video solutions
Practice questions
End of chapter exam questions.

Each video is a talk-through of an example question from the Year 1 AS Pure Maths textbook.

Both. This is useful for GCSE students such as:

high achieving students who would require stretch and a challenge
GCSE students who want to study A level Maths.

This is useful for A level students as:

a resource for teachers to set as pre-requisite knowledge
helps with fluency of key skills after the summer holidays
useful for post-16 re-sit students studying A level Maths
excellent resource for AS level Maths revision.

Of course. However, why not try the example question first to see how far you get and then watch the video to see where you got stuck or even better, check your solution.

The end of chapter exam questions are mainly AS and A level Maths exam questions and were intended for students who have completed the full syllabus and consolidated it over one or two years, rather than those starting to make the transition. More consolidation may be needed before these questions can be attempted as they are exam questions.

Yes absolutely, please fill out this feedback form to give us your opinion on how to improve this resource.

Internet-lesson in mathematics «Addition and subtraction with transition through the category»

Find the values of expressions: 2+6, 4+2, 10+5, 8+5, 10+7. Which expressions did you find easily, and which expression gave you difficulty?

In our online math lesson, we will learn how to add and subtract with jumping digits.

Presentation for the lesson Addition and subtraction within 20

First, remember the composition of the number 10

Now itself …

And more…. Remember and solve verbally:

10+3 =
10+2 =
10+6 =
10+8 =
10+5 =
10+9 =
10+7 =

Adding to ten is very easy, right?

And now let’s try to figure out how to find the value of an expression easily and simply, for example, for 9 + 2 …

How much should be added to 9 to get 10? … That’s right, 1. Take 1 from the deuce. We ROUND the number!

9+1 = 10. How much is left to add? …That’s right, 1 more. It turned out 11.

Find the values of the expressions:

9+2=
9+3=

9+4=

9+5=

9+6=

9+7=

9+8=

9+9=

Did you manage? Good girl!

Find the value of expression 8 + 3 .

How much must be added to 8 to make 10? …. That’s right, 2. 8+2 we got 10. How much more do you need to add?

That’s right, 1 more. 10+1 = 11…

Watch the video explanation again…

What conclusion can you draw? Round up the higher number!

We subtract almost the same. Only DECREASE to 10.

How much do you need to SUBTRACT from 15 to get 10? ….That’s right, 5. How much is left to subtract?…. That’s right, 3…

Watch video explanation…

To remember, watch video lessons 90 003

The whole table…

Explain how to find the sum value and difference value numbers 36 and 12?…

Two-digit addition: 21 + 9…

9 0002

Two-digit addition: 21 + 39… numbers 40 — 8

Two-digit subtraction 40 — 28

Addition and subtraction by parts

Add by parts 18 + 5 and 18 + 25

Partial subtraction 32-5 and 32-25

900 03

Subtraction by parts 41 — 3 and 41 — 23

INTERESTING! Methods of oral calculations …

And more …

Video lesson ….

Memo…

Unified State Examination in Mathematics

Previously, the grass was greener

All my life, when solving inequalities and equations in the Unified State Examination in specialized mathematics, everyone wrote ODZ (Area of Permissible Values), understanding by this the restrictions imposed on the argument by “difficult” functions of the square root type or logarithm. And there were no problems. So far, the explanations of a methodologist from the Kemerovo region have not got into the network.

Should I write “ODZ”?

The seminar of TP Trushkina, a methodologist from the Kemerovo region, made a lot of noise. It turned out that at the exam in mathematics, you can get 0 points for a task, even with the correct answer and the correct sequence of reasoning. All because of the misuse of the concept of «ODZ». The first thing that is clear is absolutely certain: if you wrote out “ODZ” “not completely”, say goodbye to points for the task. If you decide to write out only the restrictions introduced by the logarithmic function, and leave the condition for the denominator to differ from zero for later (“well, they will continue to be preserved, “the transition is equivalent””), and call these “incomplete” restrictions the word ODZ, then this is 0 points . And you could not even take on the task =(

An example of incorrect design

If you want to use equivalent transitions, use it, no one forbids it. But then you don’t need ODZ at all — work calmly through the system of conditions, and you will be happy.

An example of the correct design by an equivalent transition, without using the ODZ

Tell the children — let them throw away the ODZ!

But even with a correct, fully issued ODZ, there is a risk of running into trouble. The expert states: in school textbooks on mathematics, the concept of the range of acceptable values (ODZ) is defined only for functions. Therefore, use this concept when solving equations and inequalities is not recommended. However, the use of ODZ in inequalities and equations was actively used by university teachers, including when working with schoolchildren, gradually “migrated” into manuals and collections for preparing for the exam, and is now firmly rooted in the minds of tutors, teachers and applicants. As practice shows, completely written out restrictions on the variable under the heading “ODZ” do not lead to a decrease in scores on the USE in specialized mathematics. However, the expert does not recommend using this design.

“Colleagues, it’s better not to write anything at all; Tell the children – let them throw away the ODZ!” — so many emotions in an empty, it would seem, place.

The expert recommends imposing restrictions on the variable, while not “heading” it in any way. These are headings like “restrictions”, “conditions”, “important notes”, etc. should not be denied.

Our free

game-simulator “stress on the Unified State Examination”

What do Internet gurus say?

Experts in the field of preparing for the exam in specialized mathematics were divided in their views. Many well-known YouTube bloggers (Boris Trushin, Wild Mathing) are of the opinion that a fully issued ODZ will in no case lead to a decrease in points . However, restrictions are written out, indeed, they should be completely. That is, if you, for example, have an inequality with a logarithm, and which is also in the denominator of a fraction — please, demand that the argument of the logarithm be positive, the base is positive and different from one, and also that the denominator of your fraction be different from zero .

An example of correct and incorrect registration

The fact that you will not be reduced points for a correctly issued ODZ is also confirmed by the official methodological recommendations for assessing the performance of tasks with a detailed answer USE in profile mathematics from RosObrNadzor.

Transitions in Mathematics Education | SpringerLink

Authors:

Sections

Table of contents (1 chapter)

Front Matter

Survey on the State of the Art

About this book

Keywords

Authors and Affiliations

CREAD, ESPE Bretagne UBO, Rennes, France

IQS School of Management, Universitat Ramon Llull, Barcelona, Spain

Graduate School of Education, University of California, Berkeley, USA

Seoul National University, Seoul, Korea (Republic of)

Van den Heuvel Instituut -Room nr.

Free videos to assist the transition from GCSE to A level Maths

FAQs

Internet-lesson in mathematics «Addition and subtraction with transition through the category»

Unified State Examination in Mathematics

Previously, the grass was greener

Tell the children — let them throw away the ODZ!

Our free

What do Internet gurus say?

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