An algebra book requires a different type of reading than a novel or a short story. Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should read the sentences carefully and think about their meaning. As you read, remember that algebra builds upon itself; for example, the method of multiplying binomials that you'll study on page 200 will be useful to you on page 544. Be sure to read with a pencil and paper: Do calculations, draw sketches, and take notes.

This is the first paragraph from the section entitled Reading Your Algebra Book in the American high school textbook Algebra, Structure and Method Book 1 and also Algebra and Trigonometry, Structure and Method Book 2 both written by Brown, Dolciani, Sorgenfrey et. al.

My question concerns the relationship between the sentences

Every sentence in a math book is full of information and logically linked to the surrounding sentences. You should read the sentences carefully and think about their meaning.

My interpretation is that both careful reading and thought about the meaning should be applied to the information contained in each sentence and the logical links between sentences. Is this interpretation reasonable for a self-learning student?

• Yes, I think so. Oct 17, 2016 at 10:21
• What sort of answer are you looking for? The question is currently phrased as a yes/no question to which the answer would appear to be a simple yes.
– J W
Oct 18, 2016 at 5:38
• Isn't that explicitly what the quote says? Jan 24, 2017 at 15:28
• @Daniel R. Collins what's your opinion about the advice given in the book? Feb 19, 2017 at 19:28
• @skullpetrol: Indisputably correct. Feb 19, 2017 at 20:11

These two textbooks also have the same list of 7 "Thinking skills" in their index:

Recall and transfer

Analysis

Spatial perception

Applying concepts

Interpreting

Synthesis

Reasoning and inferrencing

These skills definitely go hand-in-hand with learning how to read a math book.

• These Critical Thinking Skills are applied within each of the various rubrics of the textbook, namely: Vocabulary, Symbols, Diagrams, Displayed Material, Reading Aids, Exercises, Tests, and Reviews. Jan 27, 2017 at 22:29
• This does not directly answer the question yet. Can you edit your answer to comment on the asked question itself a bit more? Feb 3, 2017 at 9:39

Yes you are correct. I would understand the statement in the following way:

Most Math requires the student to: a. Remember definitions (Knowledge - e.g. what is the definition of area, the formula for area) b. Understand the meaning of the concept (e.g what does "area" denote in real life) c. Apply the formula (Application - e.g. use the formula to calculate area in a specific case) and d. finally bring all these together to answer a real / word problem.

A math text book outlines the first three aspects - namely definitions and formula, some examples of how the concept is used, and some problems solved using the formula. A student would need to understand all these three aspects and then how they fit together to be able to look at a related problem and solve it. For example, if a student were to just remember the formula for area without understanding what area is, he or she would not be able to answer a problem because they are not able to identify that they need to use the area formula!

Hence it is important for students to read each sentence and understand it, and then see how it links to other sentences on that topic. That way they can build a full picture of the concept (area in our example) and have the tools to use it.

As a self-learner try to put more emphasis on the thinking of the "logical links" between sentences because of the plural form of the possessive "their" used in "their meaning."

Educating students on developing the thinking skills needed to read a math book independently is not considered to be a form of job security, as shown by the down vote. But these skills will be necessarily called upon at the college level, as explained in the link.

These two textbooks also have the same list of 7 "Thinking skills" in their index:

Recall and transfer

Analysis

Spatial perception

Applying concepts

Interpreting

Synthesis

Reasoning and inferrencing

These skills definitely go hand-in-hand with learning how to read a math book.

This is how I would group the advice given in this paragraph; along with the rubrics and the so called

• "7 thinking skills":

$$\Huge \color{navy}{\text{Reading Your Algebra Book}}$$

An algebra book requires a different type of reading than a novel or a short story.

Every sentence in a math book is full of information

$\Large \color{red}{Vocabulary}$

Important words whose meanings you'll learn are printed in heavy type.

• Recall and transfer

and

logically linked to the surrounding sentences.

$\Large\color{red}{Symbols}$

You must be able to read these symbols in order to understand algebra

• Analysis

$\Large\color{red}{Diagrams}$

They contain information that will help you understand the concepts under discussion. Study the diagrams carefully as you read the text that accompanies them.

• Spacial perception

You should read the sentences carefully

and

$\Large\color{red}{\text{Displayed Material}}$

Be sure to read and understand the material in the these boxes.

• Applying concepts

$\Large\color{red}{\text{Reading Aids}}$

• interpreting

$\Large\color{red}{Exercises,}$

• Synthesis

$\Large\color{red}{Tests,}$

• Reasoning and inferencing

$\Large\color{red}{{\text{and Reviews}}}$

a Chapter Summary that lists important ideas from the chapter.

I would say just read the book in a careful engaged manner (much more engaged than a narrative history book). And especially work all the example problems (along with the text, on paper). Also, any derivations, work the derivation on paper along with the text.

• It's not clear to me at all that one should work all the example problems, since the typical textbook deliberately (for various reasons) has many, many more exercises than are needed as diagnostic for understanding. It'd be a vast waste of time. Mar 25, 2018 at 0:50
• The example problems, not the practice problems. THe ones that are part of the textual explanation. Not the ones at the end of the section. Mar 25, 2018 at 3:10
• That said, I think working a lot of the practice problems is advisable also. I did 100% of the book's practice problems when I took calc and crushed it. Outperforming guys smarter than I. Freeman Dyson did all the DE problems in his text and Feynman learned E&M by doing every problem in the book also. (Of course there is a limit to that because we could always double the problem count...but I'm just saying...) Mar 25, 2018 at 3:12
• @guest: Note that exercise counts have increased over the years. I have an Introductory College Algebra text from 1923/1933 (Rietz/Crathorne), and a sample section tends to have 20-30 exercises. A current textbook (say, Martin-Gay, 2007) tends to have 50-100 exercises per section, and generally needs to spell everything out in vastly more detail (e.g., 300 5x8" pages vs. 700 8x11" pages). Dec 30, 2018 at 4:55