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What I learned from 20 Years of Student Journals

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NCTM 2018 Annual Conference
Washington DC
Presentation about Student Journal writing in mathematics education

Published in: Education
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What I learned from 20 Years of Student Journals

  1. 1. inspiration I remember having to slow down and show my thought process. Sometimes it was a chore and took more time than I allotted for it, however there was a sense that I was going beyond a typical experience with math. Writing about math made it more approachable. It was one of the first times that I found myself loving math. “Instead of cycling through math assignments, I feel the journal gave deeper meaning to my studies. I was never left with that all-too-common feeling of "I will never use this in real life" because I WAS using it in real life! ..and in combination with all of the other skills I was learning in school! Amazing, really. I struggled a lot with English and writing in high school, and I believe keeping a math journal helped me to be more confident when tackling writing assignments in general. It really helped to further my writing skills more than other methods, which is pretty outstanding for a math class.” “I honestly wish I could track down this journal and re-read my thought process and compare it to my current self. I think I might be surprised.” “I remember at the time I found it to be a stressful task. Which is interesting because I definitely excelled in my humanities classes more than math/science, so in hindsight I feel like I would a have appreciated the opportunity to use my language skills, but I think it was such a leap from anything I had been asked to do in math before that point that I found it foreign and intimidating.” “My math journal was something I really took pride in. To this day, I still have them. Keeping a math journal gave me the opportunity to exercise my skills in writing, math, and art/design all in one place. I will forever be grateful for your math classes and teaching methods. I never tested well as a student, but the first and only time I took the ACT I scored in the 99th percentile in Geometry..! It got me a scholarship for college. There really isn't much I remember from other classes or teaching methods throughout my time as a student, except for my math journals. The impact it made on my life is beyond words.” “I remember my improvement in the class. The first few entries were reminiscent of what I learned in math before. As someone who struggled with math but excelled with writing, I was soon able to write out my reasoning which strengthened both my understanding of and in interest in Carmel Schettino, 2018 “I am just about to enter graduate school for Art History. Writing in math class began the trend of deliberate, methodical, and passionate thinking to an extent. Of course other classes … aided with this. However, there is something to be said about writing about what would otherwise be considered a mechanical process. I feel as if I am a more careful curator now. I methodically work through my process with bursts of creativity and inspiration.” Alumni Journal Survey Responses
  2. 2. Metacognitive journaling in math: lessons from 20 years of student writing CARMEL SCHETTINO, PH.D. AVENUES: THE WORLD SCHOOL NCTM ANNUAL CONFERENCE APRIL 2018
  3. 3. inspiration handouts @SchettinoPBL http://www.carmelschettino.org/ slides
  4. 4. inspiration inspiration
  5. 5. inspiration
  6. 6. What I do - PBL An approach to curriculum and pedagogy where student learning and content material are (co)-constructed by students and teachers through mostly contextually-based problems in a discussion-based classroom where student voice, experience, and prior knowledge are valued in a non- hierarchical environment. (Schettino, 2010, 2013)
  7. 7. PBL Framework Connected Curriculum Justification not prescription Shared Authority Ownership of Knowledge Journals Making connections Journals Discussing others’ solutions and mistakes
  8. 8. inspiration journey
  9. 9. 1995-2000, 2001-2010, 2011-2017 Clear expectations and samples
  10. 10.  empowering students to see themselves as capable of participating in and being doers of mathematics  Showing Evidence of students engaging in active participation in reasoning and sense making  Showing Evidence of students striving to make Their own mathematical thinking Visible and intelligible to others  Using Multiple forms of discourse implementing equitable instructional practices : develop Positive Mathematical Identity NCTM, Catalyzing Change in High School Mathematics
  11. 11. implementing equitable instructional practices : Develop Mathematical Agency  Telling others through words and actions who they are and what their purpose is  Showing Evidence of taking risks and engaging in productive struggle  Understanding that learning results when they successfully leverage an approach that works for THEM NCTM, Catalyzing Change in High School Mathematics
  12. 12. inspiration lesson #1: grading writing is hard
  13. 13. inspiration Find 2 lattice points that are sqrt(13) units apart. So you have to find two perfect squares that add up to 13 1 12 2 11 3 10 4 9. [two perfect squares] 5 8 3^2 + 2^2 = 9 + 4 = 13 Your two numbers are 2 and 3 Up 2 over 3 Up 3 over 2 Is it possible to find lattice points that are sqrt(15) units apart. No there are no perfect squares that add up to sqrt(15)
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  16. 16. inspiration lesson #2: kids are funny
  17. 17. Some kids name their journals
  18. 18. Oops! So enlightening when you can help a student with a misunderstanding
  19. 19. inspiration mathematical writing
  20. 20. “I’m Positive it’s real” Student’s description Of the Pythagorean Theorem
  21. 21. inspiration lesson #3: they write what they think
  22. 22. inspiration
  23. 23. inspiration When I originally looked at this question, I did not understand anything about how the question was related. I understood the individual parts. I knew that I had to use the distance formula because that is how you find points that are equidistant. The distance formula is…. As we went over it in class, my partner explained to me the process to find the answers.
  24. 24. “ ” I remember in class when we were going over this one, how Pete said, ‘but how were we supposed to know how to plot the points?’ I totally felt the same way because we were both thinking about it specifically. We were waiting for the book to spoon- feed us the answer. ~Student #20 about a problem deriving the distance formula with general points (a,b) and (c,d)
  25. 25. inspiration lesson #4: they don’t always get out of it what you want
  26. 26. Mathematical writing norms
  27. 27. By focusing on personal pronouns and modality, the researchers were able to see who the text recognizes as the people associated with the mathematics
  28. 28. “Voice” of Mathematics Textbook . Herbel-Eisenman and Wagner (2007) First person pronouns, like I and we, indicate an author’s personal involvement with the mathematics. The use of the second person pronoun you, also connects the reader to the mathematics because the textbook author is speaking to the reader directly. One way the pronoun you was used suggests an “absolutist image” of mathematics, portraying mathematical activity as something that can occur on its own, without humans.
  29. 29. “ ” First-person pronouns indicate the author’s “personal involvement with the activity portrayed in the text” . For example, the use of “we” could indicate that an author is speaking with the authority of the mathematical community; it may also be used in an inclusive way so as to involve the reader in the mathematics. HERBEL-EISENMANN (2007) Textbook analysis of first person plural – does it translate to student writing?
  30. 30. Advice on writing a math paper  Unacceptable to use the plural pronoun “their” to refer to the singular “reader” or “you.”  use the pronoun “we” to refer to the mathematical community in General  “we” should not be used as a formal equivalent of “I,” and “I” should be used rarely, if at all. Kleiman (2004) http://www1.mat.uniroma1.it/people/manetti/tec2.pdf
  31. 31. Research study – Did journaling increase agency, ownership for students?  31 journals from 3 different schools – my students  Page length, number of appearances of I, we, you  Used average page length  Calculated slope of regression line for each student for I, we, you over the course of their journal  Looked for trend in growth or decline  Difficult to see patterns
  32. 32. I Slope -0.04975369458 WE Slope 0.008957307061 YOU Slope -0.00632183908
  33. 33. I Slope 0.04824561404 WE Slope -0.1040935673 YOU Slope -0.03684210526
  34. 34. Student Number Difference of Last Entry –First Entry per student
  35. 35. Difference of Last Entry –First Entry per student Student Number
  36. 36. Student Number Difference of Last Entry –First Entry per student
  37. 37. One-Way ANOVA Test on 3 (I, We, You) different pronoun differences p = 8.585 𝑥 10−5 Hypothesis test says that The results that I had could not have happened by chance
  38. 38. inspiration lesson #5: evidence that in PBL students lose their sense of “I learned” and grow in “we learned”
  39. 39. inspiration reflection
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  42. 42. inspiration Since we had done a lot of problems using the pythagorean theorem in the past I thought that I could use it in this problem. As my shows this method did not help me get any closer to t finding the height of the street lamp. I decided to wait until we discussed this problem in class to earn a more effective way to solve this problem. After our discussion in class, I now know two different way to find the solution to this problem. Will presented the first method. This method involves putting the entire diagram on a coordinate grid and using the equation of a line to find the lampost’s height. Here was the illustration of this method : [See handout]
  43. 43. inspiration lesson #6: all students are capable of deep reflection
  44. 44. inspirationlooking back
  45. 45. Alumni survey on journals Question Average Response Helpful for knowledge of content matter 3.875 Helpful at improving your written communication skills in mathematics 3.875 Helpful for sorting through your thought processes & problem solving skills 4.25 Helpful for allowing to show a strength in alternate form of assessment 4.75 Helpful at organizing your thoughts in a PBL Classroom 3.125 As you remember it, how helpful was keeping a journal for…
  46. 46. Anonymous Alum, on writing  Instead of cycling through math assignments, I feel the journal gave deeper meaning to my studies. I was never left with that all- too-common feeling of "I will never use this in real life" because I WAS using it in real life! ..and in combination with all of the other skills I was learning in school! Amazing, really. I struggled a lot with English and writing in high school, and I believe keeping a math journal helped me to be more confident when tackling writing assignments in general. It really helped to further my writing skills more than other methods, which is pretty outstanding for a math class. “ “
  47. 47. inspirationmetacognition
  48. 48. inspiration lesson #7: we do not learn from experience, we learn from reflecting on experience.
  49. 49. inspiration pblmathsummit.weebly.com 6/19 beginners workshop 6/20-21 Summit for Experienced Teachers

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