CORE STRENGTH

Why do so many students struggle with math?  Sometimes I think we are grasping at straws trying to come up with a way to get students to grasp math.  Yes, I know that students should have a variety of strategies to solve math problems, but is it not possible that this variety adds to math confusion for some?  Perhaps we are (however rightfully constructivist it is) giving students the opportunity to construct their own methods for solving math problems without making sure they have the solid foundational number sense that will aid them in the process.  Perhaps, as an example, offering up strategies like the lattice method is premature for many. 

Does the lattice method really promote understanding?  My son, who struggles with math, uses the lattice method to multiply multi-digit numbers.  If someone were to ask me if I thought the lattice method connects my son to a real understanding of multiplication, I would also have to say “no.”  It is just his preferred technique because it has brought him the most success, in terms of getting correct answers.

Where am I going with all of this?  Two words...Core Strength.  I think something core is missing.  I  believe that students who struggle with math missed something foundational in their early math learning.  The problem with current math education, in my opinion, is that we RUSH so many of our children into math arena that they simply are not ready for.  Yes, there are some kids who are brilliant with numbers from a very early age.  These kids should be able to be in math arenas that challenge them and cater to their exceptional math abilities, but that is another discussion altogether.

What is the solution? I suppose defining what deep math understanding entails is a good first step.  This has been done, in the form of a document titled “The Common Core Standards for Mathematics,” written and published by the Common Core State Standards Initiative.  Here are the links to both.

Common Core State Standards Initiative

Common Core State Standards for Mathematics

The Common Core Standards for Mathematics is written as a guide to bring deep mathematical understanding to students in the U.S.  Many states have adopted these standards.  The guide is broken down into Standards for Mathematical Practices and Standards for Mathematical Content.  The Standards for Mathematical Practices list eight areas in which students should exhibit mathematical ability.  The Standards for Mathematical Content break down what students should learn in each grade, K-12.

As a teacher, I will find the breakdown helpful in determining what is to be taught to whatever grade I end up teaching.  As a teacher, I will find the practices helpful as a means of assessing student progress and ability.  I sincerely hope that, as time goes on, these guidelines will succeed in providing foundational number sense so important to successful math progression.

Finally, in my quest to find math curriculum that is both effective and relevant to students, I have been looking into Montessori math.  I am very drawn to the Montessori philosophy and approach to learning, how they connect math to everyday life, and how they combine hands-on engagement with simultaneous integration of number operations and facts memorization.  I am wondering if Montessori methods might be the answer (or at least part of the answer) I am looking for.  I plan to do more research.  In the mean time, this link and video are worth checking out.

Montessori Math Information

Introduction to Montessori Math video

PICTURE THIS: Cooperative Learning

Picture One

Cooperative learning may look like noise.  The classroom is buzzing with activity.  Students are talking, actively discussing and sharing ideas.  There may be some debates and some differences of opinion.  There is a lot of “doing” as groups implement ideas in hands-on and engaging ways.  With all of this going on there is bound to be noise, but it is a joyful noise - or at least it should be.  How, then, does one (especially the teacher) discern whether or not this noise is indeed ‘joyful”?

Picture Two

Working toward group goals and incorporating individual accountability is key.  If these things are happening, then most likely the “noise” IS a joyful noise.  One of our class readings (which you don't absolutely need to have read to understand and contribute to this blog) points to these two main goals being necessary for effective cooperative learning to take place.  A group should be working towards a common goal through the sharing of ideas and the implementation of the steps needed to meet the goals.  In addition, each person in the group should have a role in meeting that goal.  If students are doing this, while treating each other respectfully, then they are moving forward in a positive fashion.  The teacher’s role, then, is one of facilitator, where he or she provides time and space for groups to work together and provides guidance and feedback where necessary.

Activities that students might be engaged in can range from simple “one day” activities like when a group gathers to solve one particular math problem, to a “multi-day” activity where students gather numerous times to complete a task or project.  Students might be engaged in an activity where one group works together to become “experts” in a particular aspect of a subject while other groups become “experts” in other aspects of that subject.  Each group eventually teaches the other groups what they have learned.  In addition, they learn from the expertise of the other groups. This cooperative effort can effectively enlighten an entire class on a particular subject.  Students could also be engaged in a group investigation activity of their own choosing.  This cooperative learning activity is student directed.  Students decide what they want to learn about and students define roles and responsibilities within the group.

Math is just one of the subjects that can be taught through cooperative learning.  Here is a video that discusses the subject.  Much of the focus is on teaching the process of cooperative learning but there is some commentary on math as well.  The video also touches upon the power cooperative learning has in making math relevant and meaningful to students, perhaps the most significant reason being that cooperative learning is student driven, meaning students are active learners and even teachers themselves in some cases.  It is so interesting to watch how engaged the students in this video are. 

SUBTRACTION ACTION

In our class text book (which you don't absolutely need to have read to understand or contribute to this blog) the author describes three basic uses for subtraction, taking away, separating, and comparing.  The author goes on to illustrate and model six practical uses for subtraction.  These are 1) taking away a subset from a set, 2) separating a set into two disjointed sets, 3) comparing two sets, 4) taking away part of a length, 5) separating an area into two parts, and 6) comparing two lengths.

I really like how the uses are broken down and defined for me.  It allows me to simply move on to thinking about how I could help students make connections to subtraction concepts.  The modeling and illustration in the book points to how a teacher would want to model these concepts for students so, as a teacher, I would set up manipulatives at stations for students to explore each of these uses and get practice writing down the equation or equations that would go with their particular problem/solution.  I would then move on to having the students, as the book suggests, come up with their own subtraction-based story problem and solution.

After that, as a means of reinforcing the concepts, I would try to implement some sort of project-based learning math activity, the level of involvement being appropriate to the developmental level of the students.  I mainly go off on this tangent because, from what I know, project-based learning (also known as inquiry-based learning) is a way of learning that give students ownership over their learning.  I found a few websites that are helpful for getting my brain around the concept of project-based learning in general, and project-based learning for math specifically.  Here are the links.

http://pbl-online.org/About/whatisPBL.htm

http://www.suite101.com/content/project-based-learning-activities-in-mathematics-a142678

I know that all kind of branches off into the realm of what would be learned in a method class so, for discussion purposes, I am wondering what kinds of practical uses for subtraction would students find meaningful and interesting?  In other words, why might an elementary student want to take a subset away from a set, or separate a set into two disjointed sets, or compare two sets, or take away part of a length, or separate an area into two parts, or compare two lengths?

Also, I found this video interesting.  It presents a philosophy and a few ideas on how to make math relevant for elementary students.  One of its main ideas focuses on how elementary students are not ready to connect math with "real-life" scenarios as an adult would define "real-life" scenarios.  How does that idea fit with the above question?