For my MTH 495 course I read the book *Accessible Mathematics* which addressed important topics for many mathematics teacher. At the beginning of the book it stated, “The most important variable in determining the quality of education is the teacher.” I could not agree with this statement more and the students agree with it too. Generally, when a student dislikes a class or is engaged in a class they refer to the teacher and what they are doing that is either horrible or engaging. Going through the chapters of this book, any math educator can learn about different ways to be an engaging teacher and learn about the ways of boring non effective teacher.

One of the common acts of an ineffective math teacher is assigning tons of practice problems. Now I agree the students need to practice and implement what they learn. But if a student is doing something wrong and they do it 25 times the wrong way and then you correct it once, what do you think the students will remember. Also, there is never enough time to go over all the practice problems generally assigned and it can be counterproductive. Having students memorize formulas that they are not going to remember after your class anyways is a waste of time. This class time could be spent to further conceptual understanding.

The book notes that short warm-ups can be very effective because it gets the students focused on math and is a great way to make the curriculum on going. This leads to another point of vocabulary. The incorrect math language used is commonly the source of student misconceptions and thus teachers should always be aware of how they speak. A good teacher also keeps in mind the different ways students learn and thus should incorporate multiple representations and visuals. When choosing problems for students it is very beneficial to put them into real world contexts and situation that they can relate to. Doing so engages the students and grabs their attention. To keep students interests, the book also suggest to mix it up and not always stand at the board with notes , a textbook, or a worksheet. The book suggested bringing in the book of world records and making a math lesson out of that. Creative! An effective teacher additionally, should question everything. Ask the students why, or how they got their answer, how do they know, etc. I love to questions students because it can furthers there math abilities, it can uncover misconceptions, and eventually the students will be comfortable making mistakes.

All in all, this book was very insightful. I would recommend this book to someone just beginning to learn about math education. Many of the points the book made I had heard of before so it was a smooth read for me. There were a few new ideas I gained my reading this book and for that it was worth it. As a final point, like the book stated very well, “if we want better outcomes, we can’t keep teaching the same way!”