For our first book review in MTH 495 I chose to read Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement by Steven Leinwand. The book was a wonderful short read that provided lots of information regarding teaching mathematics. Each instructional shift is an easy adjustment to make within an already established classroom, or a good foundation to start a classroom.

Most of the instructional shifts I have learned about at Grand Valley State University, so it was really beneficial to reiterate important ideas about the classroom. Leinwand did a great job of providing examples of dialogue within a classroom with and without the suggested shift. This provides a good idea of what our students are not getting out of math class and why so many students are bored with math.

Chapter 2 discussed the importance of constant review. This is one topic we did not discuss in my education classes and I found to be interesting and something I want to bring with me to my future classroom. It discusses the waste of the first few minutes of class when the teacher takes attendance, checks for homework completion, and then attempts to get class going. A simple solution and easy way to take full advantage of the short class periods is to have mini-math “quizzes” to get students minds warmed up for the rest of class. There could be 1 to 7 problems that cover topics from the first week of school or even foreshadow next weeks lesson. This provides students with a chance to master the variety of math skills. Let’s face it, its rare for a student to master something after half of a week of instruction. Plus, the teacher is able to check homework and do attendance while the students are doing this.

I specifically see my self using the idea of constant review in my future class room but adjusting it to fit the needs of the class I see my self having and to most importantly fit my students needs. I see my future class as being a very much activity based class which asks for as much time as possible for students to work on these activities. Therefore, I think I would stay away from any number of questions that exceeds 3 or 4. I believe it would be very beneficial to use the five minutes that it takes for me to take attendance as a time to have 3 questions for my students to work on. One of these questions I would pull from previously learned concepts earlier in the year. This as described above will allow for mastery of the information rather than memorizing it for the test and immediately forgetting it. The second question I would think would come from the current unit being taught to keep it fresh in my students minds. Possibly directly from the lesson previous to that days lesson just to reiterate what we learned the day prior. The third question I foresee coming from the future unit. Students I would expect to struggle and possibly have no clue how to work on this problem and I think this would be great for the class. I would anticipate the discussion of the first problem to go fairly quick because hopefully they would have it mastered. The second problem I see spending more time on simply because we would of just discussed it the day prior. The third we may not even come to a final conclusion. I see it being more meant to get the students thinking ahead so that when it comes time to actually teach that concept, students are already aware of it which I think will make the learning experience much better.

An important instructional shift Leinwand brings to our attention is having real world connections and situations for students to apply their math skills in. This will engage the students in their learning instead of falling asleep while counting down the minutes to go to phys. ed. class. With having these real world situations students can discover math and have in depth conversations amongst their peers and really learn the material. I see my self using a lot of videos to bring a real world situation into the classroom. This will get my students hooked onto that video, and then I can supply activities that feed off the video shown.

I see my classroom being a very activity and discussion based. After class activities, I would like to have class discussions about the activity where I can ask students questions such as “why?” or “how do you know?” In my experience as an educator thus far, I have found when I do this type of thing students learn a lot more. One, because students have to develop enough knowledge to be able to explain their thought process. And, secondly the students who are having trouble have multiple opportunities to hear explanations of the topic we are covering. This type of environment is tightly related to Leinwands 10th instruction shift of making “Why?” “How do you know?” and “Can you explain?” apart of your classroom mantras.

Another shift Leinwand talks about is having multiple representations. This is something I have near the top of my list as far as how I would like to teach my students. There are so many different learning styles out there and a big reason so many students don’t like math is because there teacher only stands in front of the class spewing out information that the students have no clue what it means. I am going to make it a priority to constantly give my students opportunities to draw and describe their math. The board will be a log of the class period full of pictures, tables, and number lines to give my students a visual to go off of to hopefully help them make sense of the information.

This book did a fantastic job of pointing out important shifts teacher need to make to better the learning of their students. would recommend this book to any one entering the field of teaching or even current teachers. These are 10 minor adjustments that can be made in a classroom that can make major impacts for the betterment of our students. Leinwand does a phenomenal job of portraying the importance of each.