Here is a partial list of my objections to the TERC Investigations curriculum.
1. It is at least 2 years behind where it should be. 
For example, my son's second grade class has yet to do anything beyond 1digit additions. The very last problem in the program, a word problem asking how many times 5 goes into 171 (with remainder), should be a third grade problem. TERC puts it at the very end of grade 5 as a CALCULATOR problem! 
2. Important topics are omitted or superficially brushed over. 
Mathematics is sequential. To learn it correctly one must throughly understand on level before moving on to the next (example, understand multiplication of whole numbers before plunging into multiplication of fractions). TERC covers NOTHING in depth except for whole number mental math. In particular, the treatment of measurement, geometry, and fractions  three major parts of the elemetary curriculum is completely inadequate. 
3. In the early grades progress in math is held hostage to writing skills. 
Many TERC assignments require the student to give answers in complete english sentences. This is extremely difficult for first or second graders, and completely unnecessary. Mathematics has its own notation  numbers, equations, diagrams  that are very efficent and are independent of english. Indeed those notations were developed because ordinary english is inadequate for the purpose. That mathematical language should be used and learned. 
4. The program actually contains very little mathematics. 
Yes, there are lots of activities, but those often have little mathematical content. Example assignment: 
Find a button. Write down all the words you can think of that describe your button. 
That is an assignment my son's class spent two days on. Such assignments make teachers happy since they are easy to understand and create the illusion that everyone is involved in learning. But the hours that are suppose to be spent on mathematics are often spent on something else. In fact, TERC students do a VERY limited number of problems per week. One simply cannot learn math doing 45 problems a week. TERC is a program that is only pretending to teach mathematics. 
5. Effective methods of mathematics and modes of thought are not taught. 
In fact, nothing is taught everything is left to be `discovered'.
That process is painfully slow, and leaves the students with cumbersome,
unmathematical ways of thinking and solving problems. They are left to somehow
muddle through mathematics without explanations. Because nothing is explained there is no mechanism for correcting errors, confusions, and misunderstandings. Students do not have books so never get to see efficient elegant solutions, or even correct solutions. Parents do not see any books so are unable to help, or even recognize how little their children are learning. The children are aware of this. They are unsure or what is expected and why. They do not develop confidence about their ability to do math. 
TERC students will hit a wall, probably at the end of middle school. They are not being given the grounding needed to understand the abstractions of high school algebra and geometry. Their options for careers in science and engineering are being closed off by their elementary school program. 

Thomas Parker 