Letter to teachers or other book users
Mathematics Learning
This book has been written to help teachers or parents, who want to help the children in their mathematics learning process. This present chapter is titled by Some Predictors of Mathematics Learning. The picture gives the main areas, which are used in this short introduction. We have six subtitles:
- Teaching,
- Thinking,
- Motivation,
- Interaction,
- Self-Esteem,
- and Attitudes.
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We first discuss the relationships with the different variables. As teachers we try to teach the children by using Attitudes, we have to sell our selves so that the students like their teachers. You can not sell your subject (mathematics) if they hate you. They must like you be fo re they like your mathematics. The attitudes about the teacher and the mathematics must be in order. This would mean that the interaction in the class room must function well. The students must understand that their teacher like them and is ready to help them in mathematics solving problems. That would mean that the Attitudes and the Interaction together activate the Sefl-Esteem of the students.
If the Self-Esteem is good enough the students are activated for explorative behavior, which means that they are motivated. Without motivation there is no learning. And the motivation should be intrinsic motivation. When the explorative behavior is activated it would also mean that the thinking process, which really is needed in mathematics problems, is activated. I would say that the students get also critical thinking abilities in this kind of learning process.
Mathematics Teaching
Mathematics Teaching is also very important for the teacher and her/his students. We have here a picture of some important latent variables we need in Mathematics Teaching.
The first figure contains some important variables eight to number and how to combine them. In the other picture we have six more activities we might need in the teaching process. In the first picture we have the most important starting activities and in the second picture we have the approaches how to differentiate the teaching process.
The first picture starts with the selection of an Emotional Classroom Climate. That would mean that the teacher is included in the Climate and especially Teacher Student Interaction. There is plenty of studies, which show that this kind of approach will have an impact on student Self-Esteem. We should understand that first with good Self-Esteem can a strong Motivation follow of which the good learning is the product. The route is marked with a green ar row, which should been fol lo wed. The teacher should not start the Cognitive Climate before the students have good enough Self-Esteem. Following the route, the teacher should select the Learning Theories and Learning Styles which he/she thinks would lead to best Learning.
In the Classroom there certainly are students who need Exemplification and Differentiation. Don’t forget to build a good enough Learning Environment where you have your students with different Activities. You should also have discussions with your students so that some important areas are well enough Reflected.
When planing the contents of the classroom aims and the Key Contents as given in the beginning of the lesson. The structure of the lesson should be about the same. When starting the lesson it should motivate the students for explorative behavior. It means that the students should have problems and ability to explore it.
The teaching should start with real objects, which we should use before going over to theoretical thinking level of teaching. The action level for the students is the action when they solve the problem. They do not need any objects to solve the problems.
When teacher follows this type of phase approach, then every student will get teaching on student’s own level. If the students are taught in this way they will be led to intrinsic motivation, which is the correct type of motivation.
Every lesson should include mental counting, problem solving and action parts. In this way we can be sure that every student will learn
- mechanical counting ability,
- mathematical thinking ability,
- and problem solving ability.
In this way the teaching will be internerlized. In the teaching process the teacher should always include self-estimation for the students. And it should be used quite often as it has been done in the text book.
For every lesson you should have mental counting, verbal counting, and problem solving items. The teacher should use plenty of items, which activate the students for thinking and explorative behavior. Let the students also build a mathland together, which can be used whenever needed.
The Contents of The Math book 1a
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Time Table
The teacher should think the Time Table carefully according to the student level. You can also use your own diagnostic test. Using the results of the test the teacher can plan how to work
with the contents and differentiation. When you have discussions with the parents you should also have the students as well. You plan the goals for the students with their parents and students together. It is also important to listen to the students how they like to learn mathematics. In December/January meeting with students and their parents you should discuss how the students have learnt mathematics and how you will continue in spring term. Don’t forget to encourage your students for the coming term. It is a good habit to have a good emotional interaction with the class room.
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School and Home Interaction in Mathematics
The above study of mathematics learning with Home Interaction and School Interaction was done with
N=2500. We can see in the model that Self-Esteem is one of the most important predictors of Motivation and Achievement. The next important question is what is behind the Interaction?
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When I made the Interaction theory of Learning, I got the most important ideas from Bowlby’s Attachment theory. I usually used three categories:
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The picture above shows very clearly that Interaction, Self-Esteem, and Motivation are the most important predictors of mathematics learning in the present model. The School Interaction should have an impact on the latent variables: Self-esteem, Motivation and Achievement.
Observe that there is an arrow from School Interaction towards Motivation, but the coefficient is too low. It would mean that the teacher should motivate the students by making the Self-Esteem better. Motivation should be, however, Intrinsic Motivation. Home Interaction has impacts on Self-Esteem and Motivation. They are very significant even if they are lower than the school (teacher) impacts. Especially the parental attitudes how the children like their mathematics and teacher are quite important predictors of mathematics learning.We wish you very interesting moments with your mat book and math learning.
Our Best Regards
Kaisu and Pertti
vol 111.9.2013