An Important Message To Teachers, Parents, and Students:
What are grade reviews?
The word “grade” refers to elementary school, or grade school as it was called decades ago. The word “review” suggests repetition, although certainly practice may include some extension of knowledge. The word “grade” parallels the word “middle” in MAVA Math: Middle Reviews which is a collection of reviews at the middle school level.
What is the importance of cumulative review?
Children cannot learn without cumulative review. All children, regardless of math ability, have difficulty remembering skills and concepts unless they practice them within a year as well as from year to year.
On which curriculum is this book based?
A grade level curriculum outline corresponding to the problems in this book appears after the fifth grade reviews. As no one national curriculum exists and curricula vary somewhat from school to school and book to book, this book uses a blend of common approaches.
Does this book use a developmental approach?
Yes, this book’s curriculum advances each topic from level to level. For example, Level 1 has addition of two 2-digit numbers without regrouping; then Level 2 has addition of two 2-digit numbers with regrouping. Or, Level 1 asks students to draw one line of symmetry through a figure, while Level 2 asks students to draw up to four lines of symmetry, as well as recognizing when no line of symmetry exists. Careful checking of the problems in this book has produced a logical progression of concepts and skills within each topic.
Are these topics and problems all that exist in a typical curriculum?
No, these topics and problems comprise a representative sample within the framework of the book–namely, ten problems per page in a two-column format. Especially in the higher grades, some valuable exercises, such as statistical graphs, cannot fit in the allotted space. Creating a math book that is totally comprehensive is virtually impossible. While other problems could be created, a curriculum that is too broad does not permit mastery.
Does this book’s curriculum vary dramatically in any way from those typically seen?
A significant difference is this book’s introduction of fraction multiplication in fourth grade instead of fifth. Teaching a child to simplify a fraction in fourth grade is illogical without knowing that simplification means crossing out an unneeded multiplication by one.
How is this book best used?
At one school students may study fractions in the fall, whereas at another school students in the same grade may study fractions in the spring. Thus, to make this book universally available, the review problems cover the entire grade level rather than follow the sequence of one school or another. This book is best used by starting a grade level in January of that grade, completing about one third during the second semester, completing another third during the summer, and then completing the final third during the first semester of the next school year. A typical first grader would do Level 1 Numbers 1–15 (fifteen) from January to May of first grade, Level 1 Numbers 16–29 (fourteen) from June to August, and Level 1 Numbers 30–44 (fifteen) from September to December of second grade. The supervising adult should take care to spread the reviews over the available number of weeks.
Why does this book have so many problems?
People need practice to master any skill–not only in math but also, for example, in music and sports. The MAVA Math series of textbooks provides plentiful problems, so needed by students but often unavailable.
What is the grade level of this book?
While this book aims at grades one through five, some children may begin earlier. Also, children in middle school lacking certain concepts and skills may find this book useful.
What do the headers “Level” and “Number” mean?
“Level,” a synonym for “grade,” is a more flexible word because children may work above or below grade level. “Number” simply counts the review pages. Within a level, a lower number does not imply that the review is easier than one with a higher number.
How does this book interact with MAVA Math: Number Sense?
The day is too short and the subjects are too plentiful to have adequate time in school (or home school) to learn math competently. Essential supplementary work includes practicing number sense and completing cumulative reviews. As the two approaches are different but complementary, MAVA Math: Number Sense and MAVA Math: Grade Reviews should be used concurrently.
Should students use mental math when they are able or always show full work?
Students who can use mental math and get problems consistently correct should do so. Forcing a competent child to show work will only frustrate the child and slow progress. Moreover, teaching rigid, absolute methods to talented children leads to lack of trust and understanding. However, if errors are frequent, then the supervising adult should insist that the child show more work. Evaluate the child before sacrificing flexibility, keeping in mind that more complicated problems require work by all children, especially to practice skills.
Should students complete a page before starting another page?
Because curricula vary among publishers and schools, students can omit occasional problems from a page and then return to them later. Also, students need not do the pages in order within a grade level.
Was this book field tested?
Yes, this book in draft form was field tested at an independent school with about eighteen students in each of three classes per grade. Virtually all students raised their standardized test scores, both in the national and independent school norms. Some students had very significant increases. Equally importantly, the children showed happiness toward math as they gained familiarity, comfort, and understanding.
This Q&A continues on the "Free Preview" for MAVA Math: Grade Reviews Solutions.