How to communicate mathematics in 6 easy steps
- Aim to be understood! Mathematical communication is similar to all other forms of communication – the aim is to...
- Who is your audience? How much mathematics do they know? Tailor your presentation or report towards the needs,...
- Motivate first! Then present the mathematics. Begin by highlighting the motivation for...
How do you communicate mathematical ideas to students?
Mathematical ideas can be communicated in a variety of ways using many different representations. For example, you can use verbal , written , symbolic and/or visual representation to convey or expound on a mathematical concept. Technology can also be used to teach concepts.
Why is it important to talk about mathematical concepts?
Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice.
What are the different ways to teach mathematical concepts?
For example, you can use verbal , written , symbolic and/or visual representation to convey or expound on a mathematical concept. Technology can also be used to teach concepts.
How do you communicate ideas effectively?
Let’s start at the top (as any well-thought-out explanation usually does). Here's how to #communicate #ideas effectively and clearly. Click To Tweet 1. Know your stuff As Albert Einstein once famously said “If you can’t explain it simply, you did not understand it well enough.”
What is the importance of communicating mathematically?
Communication plays an important role in making mathematics meaningful; it enables students to construct links between their informal, intuitive notions and the abstract language and symbolism of mathematics.
What is meant by mathematical communication?
Mathematical Communication Skills (MCS) refer to the students' ability to (1) arrange and link. their mathematical thinking through communication; (2) communicate their logical and clear. mathematical thinking to their friends, teachers, and others; (3) analyze and assess mathematical.
How can mathematics be a useful language of communication?
Because mathematics is the same all over the world, math can act as a universal language. A phrase or formula has the same meaning, regardless of another language that accompanies it. In this way, math helps people learn and communicate, even if other communication barriers exist.
How can mathematical ideas be represented?
As most commonly interpreted in education, mathematical representations are visible or tangible productions – such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, mathematical expressions, formulas and equations, or depictions on the screen of a computer or ...
What is mathematical communication?
Mathematical communication is similar to all other forms of communication – the aim is to effectively convey an idea. Ask yourself: what is the basic message you want to send? Aspire to share these mathematical ideas in a way that instils understanding, engagement and curiosity within your audience.
How to explain mathematics to an audience?
Audiences tend to best comprehend mathematics through the presentation of simple and contextualised examples, rather than from abstract theories. Begin with mathematical examples that are basic, comprehensible and relevant to your audience’s interests, background and abilities. If more complex mathematical concepts come later, then break the ideas down into smaller comprehensible chunks.
How does writing help in math?
Essentially, writing in mathematics—like writing in all non-literary matters—is about communicating ideas with clarity and an appropriate level of detail to make these ideas understandable and traceable. The relationship between writing in mathematics and mathematical thinking, however, is intertwined and complex. Writing represents thought, which demands conscious awareness and intention on the part of the writer (Vygotsky, 1986). A student’s writing renders his or her thinking more visible. When a student is able to express and explain her reasoning and justify her thought processes and solutions correctly in writing, it shows her command of the concept (Baxter, Woodward, & Olson, 2005; Gould, 2013). As a student moves through the levels from an absence of understanding or, perhaps worse, misunderstanding, through to mastery, she is aided by the process of writing and rewriting, and questioning and answering, wherein her conceptual understanding is embellished and embedded. Successive iterations of writing and revision (contemplation) lay down deeper layers of understanding through deliberation and analysis (Ong, 1982).
Why is writing important in math?
Bruner (1968) observed that writing and mathematics are “devices for ordering thoughts about things and thoughts about thoughts ” (p. 112). Learning to write in the context of mathematics allows students to pose questions and explore ideas (for example, “I don’t get why the angles add up to 180 degrees”). Multimodal writing provides ways for students to gain insight into abstract concepts through drawing and other means of creative expression and experimentation. It also enables students to communicate their ideas to others, including their teachers and peers. Thus, writing can provide teachers with a window into their students’ minds and what they are thinking (Ball, 1994; Bagley & Gallenberger, 1992). Teachers can read what students are writing and students’ writing is often reflective of their thinking, both their understanding and their misconceptions (Ashlock, 2006). It therefore provides a means of formative assessment (Burns, 2004), which enables the teacher to identify the point at which the student’s incomprehension led to a wrong solution (Kenney et al., 2005; Wiliam, 2011). This can enable the teacher to provide preemptive intervention, such as delivering targeted and corrective feedback and content scaffolding to further advance their students’ mathematical proficiency.
What is a social math blog?
Students can access their notes during subsequent pages and sections of the program, and can edit, delete, and flag their notes for the attention of their teacher. The social math blog, called the “Wall” allows students to post original ideas and questions for all other students to view, and to post comments on other student’s posts. The intention of the blog is to promote mathematical communication through a digital group discussion. Both of these writing features support multiple modes of communication, allowing students to create notes/posts that involve typing, writing (via a mouse), drawing, and/or inserting mathematical symbols.
How many lessons are there in MLC?
The study intervention asked each student to complete eight lessons from MLC. Students were expected to work through the six sections of each lesson, enter notes of particular types into the NotePad, or the Wall, and then to take the lesson quiz. If students did not answer at least 7 of the 10 quiz questions correctly, they repeated the lesson, although without the Real World or Games sections. The students in the grade level were assigned the same eight MLC lessons, although sometimes in different orders, and lessons chosen for each grade level were developmentally appropriate as judged by the cooperating teacher. Students were allowed to use MLC resources, such as the Dictionary, as they felt the need, except for the NotePad and the Wall, where they were required to post notes of particular types. For the first two lessons that were implemented during the study, students were asked to take at least three notes in the NotePad; specifically, students were to (1) answer the Essential Question at the end of the Real World section; (2) write one new thing they learned during the instruction and/or guided practice sections of the program; and (3) revisit up to three questions that they got wrong on the Final Quiz and explain why they missed the problem (if a student had a perfect score, then this requirement was dropped). During lessons 3 and 4, students were tasked with submitting three posts to the social math blog. These tasks were similar to the ones for the first two lessons (answer the Essential Question and write one new mathematics idea they learned); however, the third task was to post a comment on a peer’s blog post. For lessons 5 and 6, students were asked to write in their NotePad using a specific note-taking strategy intended to elicit students’ reasoning within problem solving. This strategy involved having students focus on what they are learning, only write important points, use their own words, and refer to their notes later. For lessons 7 and 8, students were free to use the NotePad or the Wall in any way they chose. The purpose of this last exercise was to see if students’ communication remained mathematics focused or turned to other types of social communication. All students were provided notecards to remind them of the various note taking tasks.
What is the purpose of the NCTM?
The US National Council for Teachers of Mathematics (NCTM) argue that students need to develop mathematical ways of thinking in STEM domains and in the real world (US NCTM, 2014). The US Common Core State Standards in Mathematics (CCSSM) similarly require students to develop mathematical thinking skills, which are distinct from the CCSSM content standards yet are intended to cut across all grade levels of the content standards (US NGA & US CCSSO, 2010). There are eight mathematical practices that we abbreviate as MP1, MP2, MP3, etc.
What is the assumption that students should be able to express themselves in writing?
A common assumption in education is that students should be able to express themselves in writing. In recent years, this expectation has expanded from its origins in the Language Arts curriculum and is ensconced in all the content areas, including mathematics. This requirement is now firmly established in curriculum standards reflected in statements such as these, drawn from the US national Common Core State Standards Initiative (US NGA & US CCSSO, 2010):
Is writing a technology?
– writing is simply not possible (Haas, 2013). These writing technologies, in and of themselves, do not necessarily have the power to determine the quality or content of students’ mathematical thinking or the clarity of the communication of their mathematical reasoning. They do, however, have the ability to change the way ‘text’ is represented (diagrams, graphs, etc.) and the quality of the visual and spatial relationship between writers (students) and the ‘text’ (Haas, 2013; Vygotsky, 1981). For example, multimodal technology tools, such as dictation and voice-activation tools that convert speech to print, programs that convert equations to graphs and descriptive text, and writing pens and tablets that allow students to draw pictures and write freely, have made writing easier and more accessible for all students, particularly for students with learning disabilities.
What is the book Teaching Students to Communicate Mathematically about?
In Teaching Students to Communicate Mathematically, the author identifies a common problem. Early on, she writes, “Too often…students receive little or no instruction on how to communicate about math effectively before they are asked to do so.” The book then sets out to provide educators the tools they need to teach students how to communicate mathematically, both conversationally and in writing.
What is the purpose of Sammons' book?
Sammons provides the tools to guide teachers’ planning to that end. The book doesn’t just say “teach communication.”. It provides bulleted lists, charts, diagrams, examples of conversations and more to assist teachers in developing students who can talk coherently about their math learning.
Understanding the Importance of Mathematical Discourse
Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice.
Establishing a Discourse-Rich Mathematics Learning Community
To engage students in productive mathematics discussions, it is important to establish a learning environment that welcomes student involvement. The first step is setting the expectation that every student will contribute to the discourse community.
Understanding Student and Teacher Roles in Mathematical Discourse
Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction.
Engaging Every Student in Mathematical Discourse
All students are mathematics language learners, regardless of their level of English language proficiency, and discourse allows ALL students to develop mathematical language.
How to practice speaking in front of a mirror?
Practice speaking in front of a mirror, the dog or the people on the bus. Record yourself speaking and play it back. Test yourself by trying to explain your concept in less than five minutes.
Why is mind mapping important?
Mind mapping (explained above) is a great precursor to writing a paper or a presentation because it helps you break big ideas down into elemental pieces and then logically structure what you want to say. Using a mind map you can visualise what should come first, and what makes more sense when it follows.
What is analogy in science?
Analogies are comparisons between unlike things that have some particular aspects in common. Traditional analogies include the eye and a camera, the heart and a pump, the brain and a computer, and the memory and a filing cabinet.vAnalogies often begin with such phrases as, “It’s just like …”, “It’s the same as …”, and “Think of it as …”.
What is the overriding objective of a conceptual level?
In the initial stages, your overriding objective is to get a point across and help people understand at a conceptual level . Strange terminology, names, or specific processes rarely matter when you’re explaining things at a conceptual level.
