Orinda Elementary Math Journals This year I will be putting energy into supporting teachers and students using math journals to record important facts, formulas, and vocabulary, informally assess where students’ skill and concept knowledge and attitudes towards math and communicate students’ problem-solving strategies and thought processes. Math Journals From the Marilyn Burns resource book, Writing in Math Class,, she says, ― Journals or logs are a way for students to keep on-going records about what they are doing and learning about any topic. Reading students’ writing for any particular day gives the teacher a general overview of the responses from a class or specific insights into a single child’s thoughts and feelings.‖ Marilyn Burns starts her journal experiences with three basic prompts: Write about what you did – descriptive – ―Today I_____________‖ Write about what you learned - descriptive and summative – ― I learned_________‖ Write about what you’re not sure about or wondering about- descriptive and summative – ―I am still not sure about __________‖ ―I am wondering about __________‖ Ms. Burns goes on to say, ― Students typically need a great deal of guidance and support to become comfortable writing in math class. Especially at the beginning of the year, I provide students with clear structures for writing assignments and give them as much encouragement as I can. With all classes, however, during the year I reinforce the purposes of writing, set structures for assignments, and offer encouragement. Some students need less structure than others. For example, when students are writing about a problem that they solved, I ask all of them to give their writing a title, the name of the math problem e.g. ―The Chop Stick Problem‖, and offer the prompt: I think the answer is _________ I think this because ________________________. OR I figured it out by _____________. Math Journal Writing Writing effectively and fluently in the math content area follows the same guidelines used for language arts-writers -Pre-writing Stage Sometimes it is important to spend some time during the pre-writing process to develop and stimulate a child’s mathematical language through discussion or problem-solving experiences. During the pre-writing stage, the following experiences are suggested to stimulate the thoughts and language that will better enable students to write and record. Real life experiences Discussion from small or whole group Small Group work Problem-solving Manipulatives Calculators
Literature-reading a story Sometimes the pre-writing stage might look like a word web below:
Faster and more efficient Answer gets big Repeated addition
Multiplication
Add equal groups
Opposite of division
Teacher’s Role with writing As children use their own language to make/record discoveries, the teacher can play an important role by helping them connect their ideas with appropriate mathematical language to strengthen their understanding of math ideas. By the time students are asked to write in their math journals, they will have enough familiarity with the language and the idea to be able to write about it. Journal structure Date every entry so that growth or lack of it, any shifting or deepening over time of concepts or skill development, any connections partial or complete between mathematical ideas can be noted for sharing with parent, for the teacher’s own on-going assessment, and the students’ ongoing self-assessment. Entries should include words and numbers certainly but not always, and also drawings, tracings, sketches, graphs, pictures, diagrams, arrows and charts. Everything entered in the journal is meant to stay and not be torn out. Assignments, entries, prompts, and problems can be cut out or cut down and glued in to avoid making journal work a drudgery of always copying things onto the journal page for the students. Journal Purposes/Possibilities Table of Contents ideas Vocabulary-words, pictures, and numbers Formulas, algorithms, procedures Anchor Problems-demo problems Problems of the Day (PODs) or of the week (POWs) On-going student check of attitudes and feelings-can be two way in nature Informal assessment of skills, concepts, and connections Focused write-up on an exploration or a question that is raised in class from an experience Feedback from small group work Autobiography
Journal writing prompts Math Autobiography Prompts o The first thing I did mathematically was probably _____________ o The first thing I remember doing mathematically was __________ o In kindergarten, when I did math, I _______________________ o In first grade, I did math by _______________________ o In 3rd grade math , I learned how to ___________________ o When I was younger, I was really good at _______________ o I used to ____________, but now I ____________________ o I am good at math when I _________________________ o Things changed for me with math when__________________ o The math I have learned outside of school is ________________ o I remember learning about_____________ in math with _________(a teacher’s name-optional) because_______________ o This is a list of math things I learned by myself and these are the list of math things that my teacher taught me. o . o . o .If you use this writing idea and fashion your own prompts that work well for students, please send them in dott@orinda.k12.ca.us First week Writing-teacher selects one, some or all of the entries below to be done during class Grade 3 “What I Already Know About Math‖ What did I learn in mathematics last year? What were the things I found easy in math last year? Where the things I found hard in math last year? What do you do when I don’t understand a problem? What are some ways that I use mathematics each day? What would I like to like to learn in mathematics this year? Grade 4 ―What I Already Know About Math‖ What is mathematics? What did I learn in mathematics last year? (give some examples) Did I like math last year? Why? How do I use math each day? Am I a good problem-solver? Why? What does a good problem-solver do and know? What do I want to learn in mathematics this year? Grade 5 ―What I Already Know About Math? What is mathematics? What did I learn in mathematics last year? (give some examples) Did I like math last year? Why?
How do I use math each day? Am I a good problem-solver? Why? What does a good problem-solver do and know? What do I want to learn in mathematics this year? What helps me learn best?
Journal entry from an exploration with commutative and associative properties Start list with 3 + 4 = 4+3 and 9 + 6 = 6+9 Can anybody add another example to the list? Build the list to 6-7 examples. Ask, ―What do you notice with these examples?‖ or ― What do these examples have in common?‖ With the description of the property coming from the students, the teacher can provide what the students probably won’t know— ―this is called the Commutative Property of Addition.‖ The same process can be followed with the Associative and Zero Properties of Addition. Regrouping is an important and complex concept used in the traditional algorithm for adding large quantities. It is important that students get ample opportunities to understand this concept with use of base-10 blocks, discussion, and exercises with representing a number in different ways (thinking flexibly about quantities) e.g. 62 is 6 tens and 2 ones or 5 tens and 12 ones or 4 tens and 22 ones (good journal entry) Journal entries for use of measuring tools with 4th or 5th graders: Write directions for a kinder to use a ruler to measure the length and width of a book. Make a list of all the different ways and tools to measure the length of an objects or the weight of objects. Record the conversion equivalents for length(metric and U.S.), liquid volume, and weight. Once students demonstrate understanding of the concept and operation of multiplication, they can work towards memorizing with construction of and access (Journal entry) to multiplication strings e.g. 3,6,9,12,15,18,…, mult. tables, 1-100 chart for pattern location, and building arrays with tiles or interlocking cubes. Journal entries for vocabulary could include shape names, attributes and sketches of various examples of the shape.