Monday, June 9, 2014

Weekly 5: Accessible Mathematics

Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement

This book by Steven Leinward takes an inside look at what education is missing and what teachers can do to provide a top-notch education for students.  Now, there is a balance.  Teachers can provide the best education for students while keeping their sanity. For teachers who go about this in the wrong way, we see exhaustion and burn out.  He says that teachers and students have the ability to perform at their highest potential if the focus is on the correct areas.  The ten instructional shifts that are addressed in this book are (with explanation):

  • Incorporate ongoing cumulative review into every day's lesson. 
    • When students are given the opportunity to refresh ideas about what they have learned, the retention rate is high.  A quick review quickly pulls students into the right mindset and they get ready to learn.  This tool can also be used as a quick assessment tool.  
  • Adapt what we know works in our reading programs and apply it to mathematics instruction.
    • There is no reason why the basics for one content area cannot translate to another.  Reading is an essential and foundational piece to a child's education.  When we can incorporate the same ideas and fundamentals, students are given more opportunities to grow.  Literal questions will demand a higher level of thinking to get students used to responding with mature and well-developed answers.  
  • Use multiple representations of mathematical entities.
    • We know that there are multiple different types of learners.  As teachers we must be able to foster all types of learning.  This is why using multiple representations can guide students' learning and understanding.  What works for one student will not always work for another.  Using differentiated instruction can help bridge the gap.  
  • Create language-rich classroom routines.
    • With more and more classroom becoming non-English, understanding mathematical language becomes tougher and tougher.  So, when students can find common ground to relate to, the understanding goes beyond language.  There is a way to present all information in a less strict and uniform way.  When students see math as instruction, their success rate decreases.  
  • Take every opportunity to support the development of number sense.
    • Number sense is the comfort with numbers that include estimation, mental math, equivalence, and on understanding place value.  This is probably the most fundamental idea to mathematics.  In order to build these thoughts, teachers must ask rich questions and introduce intriguing ideas that demand this familiarity in its responses.  
  • Build from graphs, charts and tables.
    • When we work with graphs, charts, and tables, we will most likely be dealing with real life data.  This makes the information more interpretable and understandable.  Students can use mathematical language and rich ideas when they are trying to work through these ideas. 
  • Tie the math to such questions as How big? How much? How far? to increase the natural use of measurement throughout the curriculum. 
    • The biggest tragedy in math education is that teachers most often skip the lesson on measurement.  If it is not skipped, then it is significantly neglected.  Measurement is one of the lessons that will carry students further through life than anything.  So when we are teaching this lesson to students, we must ask rich questions that lay firm foundations.  
  • Minimize what is no longer important, and teach what is important when it is appropriate to do so. 
    • There is no way that a teacher can cover a whole text book in one year.  Teachers put too much pressure on themselves to do everything.  A realistic goal is to sufficiently cover the most important topics for students.  This way, a teacher can build and plan to teach students to his/her best ability.  Students will have gained more useful knowledge if the teacher makes that decision.  
  • Embed the mathematics in realistic problems and real-world contexts.
    • Real-world problems are the best way for students to learn.  The one question that teachers are tired of hearing is "When are we going to use this?"  When students are given a real-world problems, they will automatically use mathematical language and stumble into understanding themselves.  
  • Make "Why?" "How do you know?" and "Can you explain?" classroom mantras.  
    • When students are encouraged to initiate this sense of wonder with each other, the classroom environment changes.  Students are now becoming the teachers and students are brought to the same page as everyone else.  Explaining answers puts an emphasis on the need to explain/defend a position with evidence.  
For a future teacher, some questions that might arise are:  Which of these are obtainable?  What one can I work on the most?  How many of them seem impossible?  What can benefit my students the most?  What sacrifices will I have to make to assure one of these shifts is possible?

I believe that all of these "changes" are obtainable.  This is why the author emphasizes 'shifts' because it should not be detrimental.  Theses ideas take already existing instruction and makes it better.  Teachers should always be willing to grow and change within their career.  As we gain more knowledge about the way students learn, we are figuring out the ways we should teach.  This is exactly what is happening here.  Teachers can take little steps to change for the better without adding more stress or work to their already hectic lifestyle.  My biggest takeaway from this is that most of these shifts encourage students to have more fun with learning and for teachers to incorporate more useful learning.   There is a way for students to have fun and learn at the same time.  When learning and fun occurs at the same time, success has been reached!

The hardest shift for teachers might be creating more rich and real-world examples.  This would require more prep for teachers and a deeper understanding.  Teachers must be able to foster the learning for all students.  If a student was having trouble, the teacher must understand the topic so well that the instruction might have to take a different direction to attain understanding.  Teachers need to learn to be dynamic and versatile during every part of their lesson to make instruction purposeful.  Additionally, this shift might take teachers outside of their comfort zone.  When teachers go into their own unique planning, teachers never know how students will respond or if the message of the lesson will ever successfully reach students.  The only thing that I can say is that risks might be worth the reward.  There will be lessons that fail, that is inevitable.  A few failed attempts and some tweaking might make the perfect lesson.  You just have to ask yourself:  What lesson has more utility for students?  Which one seems to be more successful?  Did students enjoy it?  If the end result is met, then the lesson is perfect.  Grow and learn from your students.  Sometimes the lesson you felt failed the most leads to the most learning opportunities.  Just know that the students will always come back and you can constantly develop your passion for teaching.  

For future and current teachers, this book can be very helpful.  Regardless of if you are in you first or fortieth year, the lessons to be learned are universal.  Like I said before, teachers should always be learning and growing.  If these shifts are already integrated in your classroom, how can they be made better?  What is the weakest one?  These shifts are just meant to maximize mathematics education.  The main goal is to make math more approachable and beneficial for students.  Who can argue with that?

Improving teachers one 'shift' at a time. 


  1. Karen, I think this book sounds like a great resource tool for teachers! How awesome would it be to pick one or two shifts a month and really focus on implementing them into the classroom?! Your explanation and review makes this sound like a book that is definitely worth reading.

  2. Good detailed summary. I also like the shift idea. As a bonus, check out one of the author's great 5 min Ignite talks:
    He's one of the few in math ed who might be able to match your energy level.