Place value understanding may seem obvious to the preservice teacher because they can name the place values. Preservice teachers need to develop a deeper understanding about how the "base-ten system is intertwined with counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. Work in the base-ten system relies on these meanings and properties, but also contributes to deepening students’ understanding of them" (Common Core Progressions, 2011).
N2.a: Recognize equivalence between place values; e.g., 10 ones equal 1 ten and 10 tens is equivalent to 1 hundred. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
N2.b: Represent a quantity for multi-digit numbers in multiple ways; e.g., number names, expanded forms.
N2.c: Contrast base-ten with examples of at least one other number system such as Roman, Babylonian, Chinese, Egyptian, Mayan, and/or a different number base (e.g., two, five, eight, twelve); units of time could also be used as a contrasting example.
N2.d: Describe advantages and disadvantages of groupable (snap cubes, digi blocks), and pre-grouped (base-ten blocks) physical models, and non-proportional models (money).
N2.e: Compare multi-digit whole numbers and record the comparisons using the symbols <, =, >. Use place value understanding to round multi-digit whole numbers to any place.
Understand place value structure by exploring other bases.
Understand place value structure as it connects to multiple algorithms.
Make connections between symbolic representations to the grouping structure.
"Deepening teachers' understanding of place value." Article in Teaching Children Mathematics vol. 13, issue 8, pgs. 434-437
"Understanding place value." Article in Teaching Children Mathematics vol. 17, issue 9, pgs. 558-567.
"Reverse and add to 100: Explorations in place value." Article in Teaching Children Mathematics vol. 22, issue 7, pgs. 404-410.
"Opportunities to develop place value." Article in Teaching Children Mathematics vol. 10, issue 2, pgs. 78-82.
Virtual Place Value Blocks for all bases 2-15
Beckmann (2017) Resources:
Chapter 1
Billstein (2016) Resources:
Section 3-1
Sowder (2017) Resources:
Chapter 2
Van De Walle (2019) Resources:
Chapter 10