Thursday, January 31, 2008

Interventions: Struggling with Basic Math Concepts

Once again I find myself turning to an article found in Educational Leadership. I have the privilege of working with dedicated teachers who put tremendous personal time into providing Safety Nets for our learners. These teachers do this at their own expense in such a selfless manner. They come in before the school day begins and they leave long after the traditional ending time...of let's round it off to say...3:30.


I recently read an article by Marilyn Burns and I believe it just might provide a spark for teachers that are always searching for that one more strategy or intervention that just could reach a child. We have all heard at some point and time phrases such as: He doesn't even know his basic math facts, What happened to knowing the multiplication tables? Borrowing...the child doesn't even have a clue as to the basic math concepts...the list goes on and on...As frustrated as teachers may sound their frustration is a faint cry when listening to the sound of frustration that is not often voiced by the child but seen in the deep recesses of their eyes.


Face it...multiplication will remain a mystery to many children because of a weak foundation linked to understanding. This produces the proverbial cycle of falling farther and farther behind other classmates. Before a child can begin to work multiplication problems they need to understand the concept and how it connects to...yes...addition. We all know that this is not an isolated case but in each classroom there exist a handful of children who are At Risk. So...what can we do to help these children?


Marilyn Burns began her quest for help by taking a look at issues that are key to teaching mathematics:



  • It's important to help students make connections among mathematical ideas so they do not see these ideas as disconnected facts. (A student can not succeed if he views multiplication facts as separate pieces of information to be memorized)


  • It's important to build students' new understandings on the foundation of their prior learning. (Sound familiar...Reading Strategy...adapt it for Math...students must use what they know about addition)


  • It's important to remember that students' correct answers, without accompanying explanations of how they reason, are not sufficient for judging mathematical understanding. (Even if a student gives a correct answer it can mask the lack of deeper understanding...memorization for memorization does not equal understanding)

All instruction must be scaffolded. Math is the same. Instruction in number sense and operations prepares our students for algebra. Marilyn Burns developed lessons that help students make sense of number and operations with attention to three important elements:





  1. Computation


  2. Number Sense


  3. Problem Solving

I love her quote that prayerfully is intended to avoid the "yours is not to question why, just invert and multiply" approach and to create lessons that are accessible to all students and that teach skills in the context of deeper understanding.



Lesson plans are developed, revised, retaught, based on student work products. Even the best of lesson plans require revisions to accommodate differentiated instruction which is a matter of necessity in any classroom. At Risk students present unique and multiple factors that contribute to their already challenging instructional needs. They may already be a minimum of one year behind and very well could lack the foundation of mathematical understanding. One can not continue to add to the foundation if it does not have the proper cornerstones or structure. The structural foundation is further weakened by the failure(s) and lack of confidence our At Risk student experience. These students require more time, supplemental instruction, and materials that are designed for their learning style and modalities.



Previously I mentioned that lessons are scaffolded. These lessons are comprised of layers and layers of strategies. At Risk students require bite size portions of scaffolded lessons to provide them with optimum learning experiences. The help and pacing is critical if student success is to be achieved. My reference to extra help is the essence of the type of help our At Risk students require. They do not just require additional practice...after all...just because you give a student 20 problems to do doesn't ensure they will be correct.



Below are nine strategies that Marilyn Burns found to be essential to successful intervention instruction for struggling math learners. Please note that the majority of these strategies will need to be applied in a supplementary setting and or in a large or small guided math group.





  1. Determine and Scaffold the Essential Mathematics Content
    (No extraneous information)...do I smell a reading strategy?


  2. Pace Lessons Carefully
    (Try to avoid...Deer in the headlight syndrome...stop when enough is enough)


  3. Build in a Routine of Support
    (Teachers should always model, Think Aloud, Model again, give an example, teacher presents another problem while this time students can turn and talk, independent work time...Oh My...adaptation of reading once again)


  4. Foster Student Interaction
    (Think-pair-share or turn and talk strategy)...are you seeing the correlation!


  5. Make Connections Explicit
    (Provide many experiences that are scaffolded and paced)


  6. Encourage Mental Calculations
    (Don't scream or pull your hair out just yet...this really does enhance number sense...they need to know what is the best way to multiply two or three numbers)


  7. Help Students Use Written Calculations to Track Thinking
    (Paper and pencil are tools for record keeping...not a crutch for negating mental math)


  8. Provide Practice
    (Not just additional practice but purposefully practice that is directly connected to students' immediate learning experiences. Provide the practice and work towards gradual release to independent work)


  9. Build in Vocabulary Instruction
    (Remember the Math Vocabulary Word Wall?...even, odd, product, factor, multiply, subtract, greater than, less than, etc...teach Math Vocabulary Explicitly and within the context of the lesson...follow up consistently and review constantly)
A strong foundation is essential for all learners. Students need to understand...Begin with the end in mind and make sure that all learners, especially At Risk Students, receive instruction that focuses on understanding, sense making, and skills. Once you begin your journey of purposeful interventions you might notice that your instructional practices follow a different path. Careful scaffolding with purposeful lessons that provide routine support will assist all students with making necessary connections. Connecting the Dots has just taken on a whole new meaning and Planting Seeds for Growth may indeed require different types of Soil and Nutrients.



Educational Leadership
November 2007
VOL. 65 NO. 3



(Because I am still a novice and haven't figured out how to post credits or quote...I want to remain in compliance and verify credits...so...portions that are italized come from the article...I will strive to improve on blogging skills...a journey worth unfolding)