# Where Does Math Instruction Begin for a 4th Grader? That is a Good Question.

photography by jimmiehomeschoolmom

A mother sent an email the other day asking which lessons of Elevated Math would be appropriate for her son.  He had finished 4th grade and was going into 5th,  but he had struggled with several of the concepts in 4th grade math.  She thought the lessons would help him strengthen his understanding, but she didn’t know which lessons to select.  “Which lessons are appropriate for 4th grade math?”  Excellent question.

Which lessons are appropriate for 6th grade math?  For 7th grade math, algebra in particular? Well, it all depends.  It depends on where the student is in his learning quest.  We would not expect a student to begin solving quadratic equations if he did not understand how to multiply two-digit by two-digit numbers, would we?  Of course not.  But knowing which lessons are appropriate for which grade level is much more difficult.  The answer lies in the scope and sequence selected for the subject by the school, school district, state or province.

Having completed alignments and correlations for districts all over the U.S., I can confirm that the content is covered in grades 4 – 9 is pretty much the same.   However, as to the order of certain topics concepts and skills and when they are introduced is a different matter.  I have heard and read concerns about the Core Curriculum Standards Initiative, but there are several benefits to having core standards, especially for the situation just described. More about that later.

More important than ‘what are the lessons for grade 4?’ is where this young fellow is in his own learning of math.  Each child is unique, so how do we find out where instruction should begin?  The key to knowing where is through assessment.  But which kind of assessment?  Formative, summative, informal, formal?   In this case diagnostic assessment is crucial.

There are many excellent formal assessment tools available, but I didn’t have access to this student.  To find out what her son has already mastered, I used a simple, informal, diagnostic assessment technique—-questioning.  The Canadian mother and I began a dialogue through email.   She was patient and determined to find help for her son.  Upon request, she had him perform small tasks or asked him to explain his understanding of certain concepts.  Then, she sent the results.  The volley continued until it came down to a 5 lesson recommendation for a start.

Now compare this process to how the school year typically starts.   Are diagnostic assessments given at the beginning of the school year in the middle grades?  If not, how is the starting place for instruction determined?   How are the summative test results from the spring of the previous school year used? There seems to be more emphasis on assessment now than ever before, but the most important phase of testing appears to be conspicuously absent.  I wonder why?