Standards Guide the construction of Learning Progressions Which are crucial in developing texts and assessments.

Standards Guide the construction of Learning Progressions Which are crucial in developing texts and assessments.

Outcomes in the high achieving countries are dramatically better than ours. Here is what the key learning progressions look like for these countries in the first three grades:

There is one more critical topic: Motion at constant speed, also in 3 rd grade. Here is the beginning discussion. Pay special attention to the problems:

We know that over 90% of the populations of the high achieving countries graduate high school, with calculus being a graduation requirement in many of them

With this 3 rd or 4 th grade material being critical for science, engineering and calculus.

Virtually everyone in the high achieving countries can handle this material by third or fourth grade. Jere Confrey and others have shown the same thing here for our students.

Place Value is a Huge Problem. In Core Standards it is far better than in most state standards though not quite at the international level.

The typical U.S. approach:

Third Grade Better than Average U.S Lesson on Place Value Note Focus on Manipulatives

Third Grade Better than Average U.S Lesson on Place Value Note Focus on Manipulatives Linear model For 10’s, area for 100’s, volume for 1000’s.?

Third Grade Better than Average U.S Lesson on Place Value Note Focus on Manipulatives Linear model For 10’s, area for 100’s, volume for 1000’s. This is Illogical and confusing

Third Grade Better than Average U.S Lesson on Place Value Note Focus on Manipulatives Linear model For 10’s, area for 100’s, volume for 1000’s. This is Illogical and confusing What represents 10,000

Third Grade Better than Average U.S Lesson on Place Value Note Focus on Manipulatives Linear model For 10’s, area for 100’s, volume for 1000’s. This is Illogical and confusing What represents 10,000 What will they make of A tesseract?

3 DIMENSIONAL PROJECTION OF THE 4 DIMENSIONAL TESSERACT Clear as a bell. Right?

This national approach to place value is codified in the U.S. curriculum to the extent that Renaissance Learning had to produce this learning progression.

Here is what the lessons and place value learning progression look like in the high achieving countries:

First Grade Russian Text: Place Value

First Grade: Russian Text: Models for Place Value. Especially note use of Decimeters for putting (2 place) Place value on number line

Second Grade: Russian Text. Note consistency Of models for higher Places and tight focus

E Even 1000’s are Consistent Consistent models make Comparison easier. Note attention to Comparisons

Note the level of The problems in the Second grade Russian Text – that’s what Proper focus does For you

Core Standards tries to reflect the international approach: This is why the key standard 1.NBT.2 is phrased: Understand that the two digits of a two- digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.”

And in the second grade standard: 2-NBT.1 we have 100 can be thought of as a bundle of ten tens — called a “hundred”

So we see that there is a great deal more going on in Core Standards than one might think: material that is subject to serious misinterpretation at this time These are the issues we hope to focus on in this session.

So we see that there is a great deal more going on in Core Standards than one might think: material that is subject to serious misinterpretation at this time These are the issues we hope to focus on in this session.