Number sense and strategies interview:

You will be choosing some number facts or other short addition or subtraction porblems to ask children to solve during an interview. You will be recording which strategies children use for which problems. As with the last interview, you will be doing individual or small group interviews with at least 5 students.

For this interview:

• You may ask non-word-problems.  Things like 4+3 and 7+6 and 14-8.  But...
  • For kindergarten if you ask an easy addition or subtraction problem (like 2+2 or 5-1) and are met with silence, you should be prepared to put it into a very simple word problem like: if you had 2 erasers and I gave you 2 more, how many erasers would you have then? or... if you had 5 grapes and you ate one of them, how many grapes would be left?
• Have counters available for kindergarten, and ready as a back-up for first grade, but we're looking mostly to see what mental math strategies children are using.
• You should have a pretty large number of problems ready to go (10-20), but you don't have to ask them all. Your  strategy while conducting the interview should be to
  • ask questions
  • if the student gives the answer immediately, record that it is a fact they have memorized
  • if the student does not answer immediately, ask them how they figured it out. 
  • record what facts they had to stop and think about, and what strategies they used to figure them out. Some of the strategies will be ones we've studied in this unit, some of them will be unique.
  • keep the interview to 5 minutes or less. 

Choosing problems:

Pick a question about childrens strategies or several related questions to focus on, and pick problems that will help you answer those questions.  Suggestions:

Which facts do the children have memorized? Video of me rambling on about this

• Kindergarten start with the facts where the whole is 10 or less.
• First grade, concentrate on addition facts
• Second grade, concentrate on the harder addition facts and on subtraction facts

Which counting strategies are children using? Another video. Hopefully useful.

• Kindergarten start with can they count up 1 or 2.  Start with small problems  If all small problems are answered immediately, try numbers such as 14+2 and 18+3.  Problems that use counting back or up by 1 are also reasonable.
• First grade start with counting on with problems like 8+3  Counting back problems where you are subtracting 1 or 2, and counting up type problems where you are counting on 1 or 2.  If there is time ask some harder subtraction facts to find out if they are extending a counting strategy to those problems or if they have a different strategy.
• Second grade questions will be the same as first grade questions, but expect more children to have most of these memorized.

Do the children know all of the doubles, and how are they using their knowledge of doubles?

First or second grade: almost all children will know the doubles to 5+5.  Ask in a randomized order the doubles for 6, 7, 8 and 9.  Ask 2-3 problems that could be solved using doubles +1 (what children if any are using the doubles to help them solve those problems). Ask 2-3 problems that could be solved using doubles +2 (what children if any are using the doubles to help them solve those problems). Ask 2-3 problems where you are subtracting using a double, such as 16-8 and 2-3 subtraction problems that are near doubles such as 15-7 (what children if any are using the doubles to help them solve those problems)? (The same problems are appropriate for both first and second graders, but more second grade children will have problems memorized or will have efficient strategies for these problems).

Do the children know all of the partners that make 10, and how are they using their knowledge of partners that make 10?

First or second grade:

• Ask questions about partners that make 10 in one or more of the following ways:
  • Ask missing number addition problems. For example: 8+___=10 (8 plus what makes 10?)
  • Ask addition problems, with the sums that make 10 hidden among other addition problems.  For example: 4+3; 8+2; 6+6; 7+3, 5+4, 9+1, 5+6, 4+6
  • Ask subtraction problems.  For example 10-2=___
• Ask a few addition problems including 10 (such as 10+4)
• Ask a few addition problems including an addend near 10 (such as 9+7 and 8+6)
• Ask a few subtraction problems where you are taking away 9 or 8