The Riley Math Model

The Riley Mathematics Model is a living document. A continually improving curriculum and process for building a quality math program at a school. As I do more research and have more experiences in schools, this plan will become more focused and detailed forever.

Continual Improvement Process

The first and most important step in building a strong math program, is to develop a continual improvement process for the management of the program. In education, we have all seen examples of trends that come and go without giving them a chance to succeed or fail. Some people hate change and some love it. Both are often too extreme. A better option is to ground yourself in a process for change. The program is continually changing, but the process for change never changes. The Riley Math Model uses the continual improvement process developed by W. Edwards Deming.

Steps toward a Continual Improvement Process:

Growth Mindset Coaching

After the Management process is in place, the next step toward a quality math program is to Coach the Teachers (and eventually the students) to a stronger Growth Mindset. Without a Growth Mindset, teachers will tend to discourage students and students will believe that their math intelligence is fixed.

Before a teacher teaches a math lesson, they must understand the brain science behind mathematical mindsets.

Principles of Math Education

This is where teachers truly learn to teach math to children. In 2014, the National Council of Teachers of Mathematics published “Principles To Actions”. This book brought together decades of math education research into the “Eight Effective Practices of Math Education”.

This includes some surprising ideas such as: Productive Struggle and teaching Concepts before Fluency. Each of the eight practices have spawned research and several well-regarded books. However, many teachers have never studied or even heard of these practices.

An important step in this process is to introduce all teachers to the eight effective practices and train them on how to use them in their classrooms.


Tier One Instruction

This is the front line of math education.

This is the classroom. Is it set up to promote a Growth Mindset? Is it set up to use the Eight Effective Practices of Math Education?

This is the curriculum. Is it aligned with standards? Does it encourage conceptual understanding before procedural fluency? Does it begin with concrete activities and then progress through representations to the abstract (CRA)? Does it inspire mathematical discourse and “Number Talk”?

my recommendations:  I recommend CPM for a project-based program.

CPM is done in cooperative study teams.  CPM is project-based with groupss doing minis projects everyday in class.  CPM has homework programed into a mixed-spaced format for mastery over time.  The book tells a story and, if followed, will report in mastery of the concepts by the end of the class.  I also often use journals for reflection and alternate activities if I know of an actvity that I feel is more effective.  I often choose activities from three-act tasks or Desmos or Open-middle problems.

This is the lessons. Are we using effective and rich activities to promote learning and develop mathematical mindsets? Can we find more effective activities (spoiler alert…yes)? It is my experience that, other than some online math games, all math resources have good points and bad points. Your Continual Improvement Process will find the good points and reject the bad points to find what is most effective for your students.

This is formative and summative assessment. Does it measure success? Does it allow teachers to make good and real-time decisions?  Is homework being done for the right reasons and for the right person Per “BUILDING THINKING CLASSROOMS” (BTC),  I have rebranded homework as “Check your understanding” because the research done for BTC shows that students will be more inclined to do it for their own understanding and for the right reason (understanding). 

This is where the Magic Happens.

All of our efforts should be focused on making Tier One Instruction as effective as we can make it.  The right activity at the right time with the right focas and the right amount of support.

Tier Two Instruction

When it is determined that the Tier One Classroom environment is not allowing a student to master the concepts and progress, Tier two should be used to correct the situation.

Tier Two Instruction requires specialized training to help students get back on track with the rest of the class. Remember, all students can learn math to the highest levels. Some will need extra help and Tier Two Interventionists will need training in how to give this extra help.

There are at least three reasons why students may not be progressing in Tier One.

  1. A weak Growth Mindset
  2. Poor Organization Skills
  3. Gaps in their math knowledge

In my experience, a weak growth mindset is the main reason why a student might not be keeping up with their classmates. Coaching them to a growth mindset and showing them some success to build their confidence can do amazing things and help make tier one instruction effective.  I use the practices described in the book “Coaching for a growth mindset”.  It is important that both students and teachers have a growth mindset.

Sometimes students work hard and believe they can learn, but they struggle with organization skills such as taking and maintaining good notes or even keeping track of homework assignments. Tier Two is a great place to help them develop and respect good organization skills.

Sometimes students are hard workers with good organization, but the material is just too far over their heads for them to keep up do to gaps in their skills. This can happen for many reasons. Often it happens with a transfer student or a student with heavy absenteeism who missed some key ideas and it is now a stumbling block for them.  I like to do intervention with students in small groups of three or four with open activities that are concrete and allow them to be creative with the math and wishin the framework of math and recognize connections to other math concepts they have learned.  Concrete learning is often neglected in order to move rapidly to abstract learning.  I like to go back to Concrete learning and let them be creative with it.  I have had some excellent success with this approach. All Interventionists must have a strong Growth Mindset.

All three of these areas can and should be addressed together.

Tier Two can sometimes be a quick intervention in a small group. Other times, it may be a longer term intervention with a detailed plan to help the student get back on track and develop a stronger math mindset.

If it is determined that the student is not learning in Tier One, they should be pulled out and given Tier Two support. Class time should not be wasted if at all possible.  It has been my experience that we often leave students in tier one environments where (due to gas or mindset), they get further and further behind and the class time is not only wasted, it is actually causing harm.



Building Thinking Classrooms (BTC)

BTC published in 2021, BTC addresses some old classroom practices with extensive and surprising research for tier one instruciotn to maximize the amount of time students are thinking. For example; - Students work best on their feet at vertical surfaces in groups of three. - Groups should be assigned frequently and randomly. - The front of the room should not be apparent. - Tables should point in all directions in a defronted room. - homework should be rebranded as "Check your understanding". - Knowledge should be allowed to move around the room from group to group

Tier Three Instruction

Tier Three instruction is for students who require long term intervention. This includes students with learning deficits that require specialized and personalized instruction. Again, all students can learn math to the highest levels.  Some my need more support than others.

Anyone providing Tier Three Instruction should be a licensed specialist. They should have specialized training and, within this training, they should study the concepts of growth mindset coaching and the eight effective practices of math education.