Focal Points are the Most Important Development in Math EducationIn the Last 20 or More Years

There are six topics students need to learn in K-7 – they must be learned to mastery

Core processes (algebra)

Functions and equations

Measurement and basic geometry

Numbers, number operations and place value

Fractions and decimals

Ratios, rates, percents and proportions

There is Much More to Focused Instruction than Limiting Topics

The individual lessons must focus on mathematics, rather than vocabulary,

factoids or other distractions.

Kindergarten:Typical U.S.Lesson fromAbove averageProgram

Note that the lessonIs not focused, Concepts are diffusedBy vocabulary.

These issues are universal in early grade U.S. curricula

Children have no recourse but straight memorization

In Stark Contrast Here are Corresponding Lessons from Russian Curriculum

First few lessonsFrom first gradeRussian text: Progenitor for Almost all programsIn high achievingcountries

There are noWords, just 2 keyConcepts andThe corresponding Math symbols, notvocabulary

The quickintroductionOf key conceptsTakes advantageOf fact that smallNumbers areBasically hardwired

Again, note absenceOf anything but Math concepts andSymbols

But there is even more here mathematically

The underlying mathematics in the development of the properties of the whole numbers is the Peano axioms in the Russian system

There is a mathematical reason for every step and every concept. Moreover, they are known to be the core steps and concepts.

Third GradeBetter than Average U.SLesson on Place Value

Note multiipleFoci, places andSeparate Manipulatives:Linear modelFor 10’s, area for100’s, volume for1000’s

First Grade RussianText: Place Value

Note the level ofProblems associatedTo this lesson

First Grade: RussianText: Models forPlace Value.

Especially note use ofDecimeters for putting(2 place) Place valueon number line

Second Grade: RussianText. Note consistencyOf models for higherPlaces and tight focus

E

Even 1000’s areConsistent

Consistent models makeComparison easier.Note attention toComparisons

Note the level ofThe problems in theSecond grade RussianText – that’s whatProper focus doesFor you