Tuesday, June 28, 2016

Funneling vs Focusing Questions FAME Article Responses

Our first assignment of our FAME program is reading the following article, Questioning our Patterns of Questioning: http://www.svmimac.org/images/SVMIPD.091312.Questioning_our_Patterns.pdf


A1: Funneling reminds me of talking to a student about solving linear equations. What operations do you see? "How can we get rid of that?" And so on. It reminds me of asking a few too many leading questions.

I try to relay it back to the formative assessment lesson. The story of x where you are building an equation starting with a solution. An equation is undone to find the value of x.

Focusing questions are in direct response to how a student is thinking, rather than how I am thinking of the problem. The most common focusing question could even be "What do you notice?"

Focusing questions remind me of math talk moves. I model and want students to rephrase what other students have said. I also want them to acknowledge another person's thinking by naming their method. Paraphrasing a person's method. 

And the mother of all talk moves.. not talking. Wait time. In the dialogue of focusing questions about slope the teacher let the students pause, to ask other students if they AGREED or DISAGREED with the thinking. I know we have to bite our lips sometimes to try to not say what another student is ready or could say.

Q2: What opportunities does a focusing pattern of questioning afford us that a funneling pattern does not?

A2: Focusing questions allow opportunities for students to contribute their thoughts to the class discussion giving enough wait time. Funneling questions also tend to have few students raising their hand to begin talking about a topic. Focusing questions seem to be a majority of intuitive responses. Focusing questions can spark or synthesize a conversation. Patterns of funneling questions can tend to be tuned out by student(s).

 Q3: What are the key features of the two questioning patterns described? How do they differ?

In general, questions are a big part of engaging students in discussions. Classroom questions tend to follow the IRF, Initiation-Response-Feedback model. I think funneling questions have feedback that is telling the students whether they are right or wrong. A focusing question is a response that opens it up to other students to confirm or deny the validity of the response.

One of the main characteristics of funneling is the teacher is doing most of the cognitive work. The students are simply responding. When students are encouraged to connect their thinking with their peer's ideas there is more cognitive demand on the student.

Tuesday, June 14, 2016

Letters to Everly Rose Joyce

The last 3 weeks of school I was on paternity leave. When students finished a lesson with the sub one day they made some letters for my daughter, Everly Rose Joyce, born May 28th, 2016. I emailed a picture of her to the staff the day after she was born and they broadcasted it on our televised KTLR student news network. It meant a lot to me. I'm not going to save the best one for last, I have to share the one that blew me away below. It was a sheet of copy paper folded into fourths and the front was below. Amazing lettering and drawings of roses. The best part though was inside, where Tiffany went into personal details about what characteristics I will try to teach her and instill in her that I tried instilling in my students. Wow.
She writes really small, but the words had a large impact on me.

Alex illustrated his math joke I told my Facebook friends. What does a mermaid wear to math class? An algae bra.

Chloe and Marina want to modify Everly's name a little bit. LOL.

A group collaboration with comics. Davin also gave me a sound cloud link where he apparently is performing a song that is remixed as dub step he said..? I will be sure to post it for all to see.

I wanted to post the inside of this card because she thinks Everly will be a "#mathgenius"

This was hilarious. Harrison said my daughter will learn how to be tactful, to have no excuses, and turn out a little... red. (because I'm Irish and when I laugh too hard or get mad or embarrassed I can get red) Also, that leaf is not broccoli he said, it's a shamrock, HAHA.

Rasheed and I are both huge Warriors fans. He got the colors spot on here.

Third period had everyone sign a card.
This was an amazing quilting job in a valentine's day color theme. Beautiful.

This was nice to read these, especially bringing up my spirits after hearing of the overall loudness of classes while I was gone and certain students being extra difficult while I was gone.

Monday, June 13, 2016

Trimester 3 Final Scoring & Reflection

The audience I am directing this blog post towards consists of my students, their parents, and fellow teachers. For students, I want you to see the answers to the Trimester 3 Final and see how points were given. Parents, same idea. This also can give you an idea of some topics you might want to study prior to next year. I also recommend the free Jo Boaler course How to Learn Math at Stanford that is self paced, online, and can be taken this summer.

My third audience is teachers. I want to improve my assessment questions. I also know this final was too length for a 53 minute period, which also influenced how I scored it. I also would like feedback on what DOK, or Depth of Knowledge, level you feel most of the questions are. The first test is Common Core math 8 and the second one is Common Core Algebra.

My last purpose of this blog post is to write down some of my thoughts of where I feel the most common mistakes were made.

A parent earlier this year was not happy with the grading of a trimester final test, and how getting some questions correct, though still under 50%, earned him a 0 on a 4 point scale. A colleague recommended this scale which I will use to grade this final. Here is the comparison:

The final was also lengthy. So, the test was out of 48 points which means 0-12 wrong is a 4, 13-18 is a 3, 19 to 23 wrong is a 2, 24-35 is a 1, and 36-48 is a 0.

Once again, the biggest mistakes with identifying the slopes of lines was forgetting the negative sign for a line that was decreasing from left to right. We watched the Slope dude video, which students enjoyed, but it didn't stop students from forgetting the negative sign. Also, the question should have asked the relationship between lines C and D to get at the fact that they were parallel because they had the same growth but different y intercepts.

Students were assessed on scientific notation to decimal notation and vice versa. Also, multiplying and dividing numbers in scientific notation. A lot of students resorted to the inefficient method of converting to decimal, multiplying, and then going back to scientific notation. They also worked on power of a power rule and multiplying power numbers.

Then students were assessed on angle vocabulary. Surprisingly, students struggle a lot with the 7th grade concept of vertical angles. Not sure why.

Question 5 assessed identifying whether a graph or set of points were a function or not. I was looking for students to say, for example, the circle is not a function because the input (x) 0, has outputs of 1 and -1, so it's not a function.

Then they were assessed on writing an equation given 3 triangles angles as algebraic expressions. They were also assessed on exterior angle theorem. Students struggled with the definition: the SUM of the remote interior angles is equal to the measure of the exterior angle.

Finally on this page, students determined if 3 side lengths formed a triangle, and if so what type of triangle. Some students forgot to square the numbers to determine the side length, and some are still tricked when the small and medium sides added together equal the longest side (this would not form a triangle)

Then they were assessed on approximating a rational number to the nearest tenth using a number line. It's a mult-step process that students can get lost in sometimes. Then there were pythagorean theorem missing leg and hypotenuse problems following a fill in the blank definition, where modified tests were given a word bank to use for the definition. The last part there is finding the distance between two coordinates. Sadly, the biggest problem here was students graphing the point (0,-1) as (-1,0)....

Then students cubed a number, and cube rooted a number. They found the surface area and volume of a cube given a side length. Students get confused about the units being squared or cubic here. Finally, they find the 2 consecutive integers the side length of a cube with a volume of 83 cubic units is between.

Here is where students were assessed on topics that were closer to the end of the year but we didn't get enough practice. The standards say students need to KNOW the formulas for cylinder, sphere, and cone volume and apply them. Finally, the last question was a review from earlier where equations have no solution, infinite, or one solution. Students struggled with fraction elimination and keeping their negative and positive signs correct with distributive property.

For the accelerated class, I will take a similar approach but not the same. That was out of 42 points, so let's say 0-8 wrong is a 4, 9-17 is a 3, 18 to 26 wrong is a 2, 27 to 35 wrong is a 1, and 36 or more wrong is a 0.

Students struggle with factoring out common factors first before factoring what's in the parentheses. Then they factor what is in the parentheses and forget to leave the common factor outside the parentheses.

Then students wrote exponential equations given two coordinates and solving the system to find the equation. Then they solved for x by completing the square. When factoring x^2-6x+9, MANY students factored it as (x+3)^2 instead of (x-3)^2. Next year we will work more about noticing the differences between different types of perfect square trinomials before notes on completing the square. Algebra tiles were not enough this year. Thanks to Sarah from Math Equals Love (google it) for the notes. Then they were assessed on using the quadratic equation. I feel they did pretty well on that.
On this 3rd page, students solved inequalities and graphed the solution, if possible. Having inequalities or equations when the boundary point or solution is zero is always tricky for some students. Also, some students did not internalize the reversing of the inequality sign when dividing by a negative on both sides of the inequality.

Then they graphed a system of inequalities where I paid attention to the dashed or solid lines, and the region that was shaded. Then students made a 2 way frequency table. Next year I will stress conditional frequency, when the probability is out of one of the marginal frequencies.
Students solved some equations by rewriting them in a simpler form. It was mostly reversing the order of operations. Undoing a square root seemed to be tricky for some. Then students graphed a quadratic and linear equation then solved it as a system to confirm the intersection points on the graph.
Towards the end of the year students worked on transformations of functions. They worked in separate groups and gave feedback on each others posters. I don't think I had them practice it enough after taking group notes about it. Then students made a combination box plot histogram. The biggest misunderstanding seems to be with histogram bin widths. They should be marked off by 5's. But between 0 and 5, there's 3 and 5. But you only include numbers UNDER 5 and at least 0. So, it's only 1 unit tall. The 5 goes in the second interval 5 and above but less than 10.

In the reflections, like I anticipated, students said they didn't get enough time on the test, which I apologize for. My concern was students finishing early with the sub and being disruptive to students still taking the test, so while I wish I shortened it, it wasn't the worse thing in the world to have it be long.

Students liked the ability to retake assessments. They did feel that they were a big part of the grade at 50%, but appreciated how a retake could positively effect their grade. Students were concerned that they liked and got used to the system, and worried that in high school their teachers would not allow this or have a system like this.

Homework was worth 0%, so a majority of students did not do it. I did require proof of some homework completed to qualify for a retake. Students said that they feel they'd do better on the tests if they had done the homework. They admitted that since homework wasn't part of their grade, they were not motivated to do it.

This was my first year not checking and/or grading homework. It was less stressful for myself and students. I'm having debates on twitter with other teachers though, because parents and myself are concerned that their work habits in high school will suffer because homework will be part of their grade.

Students liked the group work for the most part, but I think they appreciated more variety. I think I did a bit too much group work, and next year will structure more independent and partner work. I want to try the sage and scribe strategy again, where 1 partner talks out the steps of the problem while the scribe writes it down without saying anything. Then they reverse roles, and do the same problem if the scribe disagrees with how the problem was solved.

So, students, parents, and fellow teachers. Please give me constructive feedback on how questions could be improved, or perhaps if some of these questions are not fully aligned to the Common core standards, which I believe they are.