The goal of the interviews is to better understand where students are in relationship to the Research Theme and Content Goal. Interviews help us anticipate what dispositions and strategies students bring to the lesson.

In later stages of the research lesson process, interviews may be used to try out parts of the lesson. After the lesson is taught, students may be interviewed for: clarification of their thinking during the lesson, assessment of progress being made with focus students, and/or uncovering of student perceptions of what was learned.

Often test results tell us that students don't understand, but we don't know why, whether it is a learning gap, fragile understanding, or misconception. Student interviews help to identify the "why". Once we understand why students are struggling, we are better able to conceive and build a lesson. The interviews prepare us to anticipate students' responses to the lesson.

We study the mathematics students can call upon and their mathematical agency (willingness to engage), authority (decision making, authoring ideas, reasoning), and identity (how they see themselves as a doer and learner). Adding to this a second TRU dimension, productive struggle, we observe how students handle the challenges of accessing problems, moving flexibly between strategies, solving the problem, and articulating their thinking along the way..

We have found several beneficial side-effects of the interviews, students gain confidence, begin to adopt teacher questions in discourse with their peers, feel a sense of ownership of the lesson they helped with, and ask to be interviewed again.

Lesson Study teams identify a focus group of students i.e., low identity, language learners, female, students who don't take learning risks. We choose three students from each class for teachers to study throughout the year. These students are carefully observed by their teacher, interviewed more than once, and observed during the research lesson.

During the interview, students are asked to reflect on their self-perception of themselves as a math student as well as trying a math task that is similar to the one that will be used for the lesson.

- Observing teachers take notes using professional noticing skills (attending, interpreting, responding - Jacob, Lamb, Phillip). Attending - How did the student access the problem? - What strategies did the student use? - How did the student articulate his/her thinking? - Where did the student struggle?

Interpreting - How does the student see him/herself as a doer and learner of mathematics? - What mathematics did they need to employ those strategies? - What Maker Ethos is evident: iteration, revision, improvement?

Sixth Grade, Measuring, Precision (September 2015, Spool Task

AC = teacher, CW = teacher Rosa = student

Line | Time | Initial | Quote |

1 2 | 02:52 | AC | OK. When you said about six feet and eleven feet were you talking about your feet or actually inches? |

3 | Rosa | My feet | |

4 5 | AC | Your feet. How many feet with actual inches do you think that is? | |

6 | 03:11 | Rosa | Like about..... |

7 | AC | Starting from where you dropped it. | |

8 | 01:47 | Rosa | Well. Like about ... just like the feet on the rulers? |

9 | AC | Hm....hm... | |

10 | Rosa | Oh, that would be three. | |

11 | 03:30 | AC | About three feet |

12 | Rosa | Yeah | |

13 14 | AC | There're some rulers over there. Do you want to go check them out? | |

15 | Rosa | I'm used to the big ones. | |

16 | 03:50 | CW | You said you're used to the big one, what did you mean? |

17 | Rosa | Like the big, big ones. Like this big (hold arms out) | |

18 | 03:56 | AC | Oh, so how big is the big one? Is that a foot? |

19 | Rosa | I think those are thirty-six | |

20 | AC | Those are thirty-six what? | |

21 | Rosa | Inches no yards. | |

22 | 04:04 | AC | Yards? |

23 | Rosa | No, something. I'm getting confused. | |

24 | AC | OK. So how big is the big one? Do you know? Thirty-six... | |

25 | Rosa | Yards, I think. | |

26 | AC | OK. How much is that one (12 inch ruler)? | |

27 | 04:22 | Rosa | This is 12 inches. |

28 | AC | OK. So what happens when I put two together? | |

29 | Rosa | That would be twenty-four. | |

30 | AC | What happens when I put three together? | |

31 | Rosa | Thirty-six. Yeah. | |

32 | 04:29 | AC | Yeah. OK. All right. Go check it out. |

This interview makes visible a student who is not clear about the measurement units and labels for those units. Rosa has the willingness to engage (agency) in the task and is working to make sense of the methods (authoring) what path to measure, what units to use - moving from non-standard units - her feet - to standard units of measure - inches, feet and yards. |

Student interviews provide details about strengths and weaknesses across students that need to be addressed when constructing a research lesson that has a high cognitive demand emphasizing productive struggle, mathematics, access and equity, as well as agency, authority and identity.

By digitally recording the interviews, student thinking can be reviewed for different purposes. Watching the first time for mathematics, the second time for language usage, the third time for representations, the fourth time for agency, identity and authority.

- Time (about 20-40 minutes for each interview)
- A place
to interview that is relatively noise and interruption free
- The interview questions and task (posted in Files).
- Materials for task
- Paper
and felt pens for student use that will show up on camera
- Problem solving tools – an appropriate variety for student choice
- Digital recording resources: camera with film or data card, tripod, microphones,
- Google file to enter student responses

For interviews, it’s important to maintain the focus on assessing students. It is difficult to conduct an assessment
interview without employing our typical teaching moves – asking leading
questions, suggesting alternative strategies, indicating approval or disapproval about their work. Please try!

- Obtain permission slips from parents to film the interviews - schools may have generic permission slips so you only need to check to see if signed or not. Collect for whole class so can record the research lesson.
- Schedule room (library, conference room, empty classroom), set time, reserve recording equipment.

- Download the Make the Way interview
- Team members solve the problem(s) individually and discuss with group. This puts the focus on what students need to think about as they solve the problem, and it creates a group expert model for the solution path.
- Decide on follow up prompts: Please tell us what you are doing. Is there another way? What are you thinking about? How do you know? What does that mean? Can you explain it another way? Why does that (not) work?
- Collect materials / tools to be available for students to use

- Each teacher will individually interview their students recording both with video tape and entering student responses in Google template
- Teacher explains to student the purpose of interview is to learn how to be a better teacher.
- A seat facing the camera is set aside for the student

- The student is asked to think
out loud. If this doesn’t happen easily,
at certain points ask the student to explain their thinking e.g., Where did
that number come from? What does that
mean?
- It is important to give the student enough wait time (seems very long to adults in room).

Consider

- How does the student see him/herself as a doer and learner of mathematics?
- What strategies did the student use? (attending)
- What mathematics did they need to employ those strategies? (interpreting)
- What Maker Ethos did they use: iteration, revision, improvement?

- At the end of the interview the observing teachers ask the student other questions.

**Deliverable 9**. Videos of student interviews. Deliver to Brent Jackson by September 26, 2016 to post for team to view. Due: October 29, 2016**Deliverable 10.**Interview records student responses in Google template during interviews (insert Web address). Due: October 29, 2016.

Student is thanked and given
the opportunity to ask the teachers questions, and then returned to class.

**Deliverable 11.**Student work from interviews. Post and label with: Teacher initials_Student initials_Interview_Date. Due October 29, 2016.

Process is repeated for other focus group students.

Step 5: Debrief

- Add to the Cognitive Demand/Productive Struggle rubric for each student and re-post changing dates

**Deliverable 9**. Videos of student interviews. Deliver to Brent Jackson by September 26, 2016 to post for team to view. Due: October 29, 2016**Deliverable 10.**Interview records student responses in Google template during interviews (insert Web address). Due: October 29, 2016.**Deliverable 11**. Student work from interviews. Post and label with: Teacher initials_Student initials_Interview_Date. Due October 29, 2016.**Deliverables**for Focus Phase, Collaborative Lesson Research proposal #4 Research Theme, Goals of the Unit, #5 Goals of the lesson and #7 Background and Rationale for Research Theme and Content Goal, #11 Anticipating student responses

- Bird
walking – students say something interesting but off track and you are curious
about their thinking. Solution is to
wait until the end of the interview to follow the interesting thought.
- Teaching
rather than assessing … it’s hard not to teach especially with the rare
opportunity of working one on one with a student. Try to remember it’s not a tutoring session
and if you must teach, note the spot where the assessing ends and the teaching
begins.
- We have NOT found it problematic if the student does a task in the interview and again in the classroom lesson. We have found that this gives the student both agency and authority during the classroom lesson.

- Baldinger, E., & Louie., N. TRU Math conversation guide: A tool for teaching learning and growth. Berkeley, CA & E. Lansing, MI: Graduate School of Education, University of California, Berkeley & College of Education, Michigan State University. Retrieved from: Http://ats.berkeley.edu/tools;html and/or http://map.mathshell.org/materials/pd.php.
- Battista, M. (2012) Cognition-Based Assessment & Teaching of Geometric Measurement, Building on Students' Reasoning. Heinemann.
- Buschman, Larry (2001, December). Using student
interviews to guide classroom instruction: An action research project.
*Teaching Children Mathematics. 222-227.* - Davis, R. B., Maher, C. A., & Martino, A.
(1992). Using videotapes to study the construction of mathematical knowledge of
individual children working in groups. Journal of Science, Education and
Technology, 1(3), 177–189.
- Ellemor-Collins, D.L., Wright, R.J. (2008,
September). Assessing student thinking about arithmetic: Videotaped interviews.
*Teaching Children Mathematics*. 106-111. - Empson, S.B. (2003). Low-performing students
and teaching fractions for understanding: An interactional analysis.
*Journal for Research in Mathematics education 34(4).*395-343. - Fernandez,A., Anhalt, C.O, Civil, M.(2009, October). Mathematical interviews to assess Latino
students.
*Teaching Children Mathematics*. 162-169. - Jacobs, V.R., Ambrose, L.C.,Brown, D. (2006,February) Using
teacher-produced videotapes of student
interviews as discussion catalysts.
*Teaching Children Mathematics. 276-281.* - Labinowicz, E. (1985). Assessing for learning:The interview
method
*. Arithmetic Teacher*34. 22-25. - Mulder, S, Yaar, Z. (2007). The user is always right: A practical guide to creating and using personas for the web. Berkeley, CA.
- Sherin,M., Jacobs, V., Philippe, R. eds. (2011) Mathematics Teacher Noticing: Seeing Through Teacher Eyes. Routledge
- Weaver, F.J. (1955, October). Big dividends
from small interviews.
*Arithmetic teacher 2, 40-47.*