Paul's copy of Blathnaid's copy of Blathnaid's copy of Complex numbers

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Paul Molloy 6 years, 4 months ago

Created this as a copy of Blathnaid's copy of Blathnaid's copy of Complex numbers.

Name	Status	Author	Last Modified
Complex numbers	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
MATH6005 Complex numbers	draft	Julie Crowley	26/07/2016 12:53
Complex numbers	draft	Henrik Skov Midtiby	16/06/2016 11:52
Henrik Skov's copy of Complex numbers	draft	Henrik Skov Midtiby	07/07/2016 11:41
Nick's copy of Henrik Skov's copy of Complex numbers	draft	Nick McCullen	17/08/2016 11:55
Complex Arithmetic I & II, Argument and Modulus of Compex Numbers	draft	Denis Flynn	24/01/2017 12:21
MATH6005 Complex numbers	draft	Violeta CIT	06/08/2017 21:08
WM104 in-class assessment: part (i) - complex numbers	draft	Shaheen Charlwood	19/02/2020 14:20
Complex numbers Demo	Ready to use	seb SEE	10/11/2017 15:25
Blathnaid's copy of Complex numbers	draft	Blathnaid Sheridan	15/08/2018 12:07
Blathnaid's copy of Blathnaid's copy of Complex numbers	draft	Blathnaid Sheridan	27/08/2018 11:03
Paul's copy of Blathnaid's copy of Blathnaid's copy of Complex numbers	draft	Paul Molloy	13/11/2018 13:26
Maria's copy of Complex numbers Demo	draft	Maria Aneiros	23/05/2019 02:22
Maria's copy of Complex numbers	draft	Maria Aneiros	23/05/2019 03:10

There are 15 other versions that do you not have access to.

Question groups

Group 13 questions

1.
draft

Elementary examples of multiplication and addition of complex numbers. Four parts.
2.
Ready to use

Multiplication and addition of complex numbers. Four parts.
3.
Ready to use

Inverse and division of complex numbers. Four parts.
4.
draft

Composite multiplication and division of complex numbers. Two parts.
5.
draft

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$ . Four parts.
6.
Ready to use

Find modulus and argument of the complex number $z_1$ and find the $n$ th roots of $z_1$ where $n=5,\;6$ or $7$ .
7.
draft

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.
8.
Ready to use

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.
9.
Ready to use

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!
10.
Has some problems

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.
11.
Ready to use

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.
12.
Has some problems

Finding the distance between two complex numbers using the modulus of their difference. Three parts.
13.
Has some problems

Finding the modulus of four complex numbers; includes finding the modulus of a product, a power and a quotient.

Topics

No topics have been defined.

Diagnostic algorithm

Extend built-in algorithm?

Base diagnostic algorithm

state (Produces the initial value of the state object): // should be renamed "initial_state"
    [
        "topics": map(
            [
                "topic": topic,
                "status": "unknown" // "unknown", "passed", or "failed"
            ],
            topic,
            values(topics)
        ),
        "retries": 3,
        "finished": false,
    ]

topics_by_objective (A dictionary mapping a learning objective name to a list of indices of topics):
    dict(map(
        let(
            ltopics, values(topics),
            indices, filter(lo["name"] in ltopics[j]["learning_objectives"], j, 0..len(ltopics)-1),
            [lo["name"],indices]
        ),
        lo,
        learning_objectives
    ))

unknown_topics (Which topics are still unknown?): 
    map(x["topic"],x,filter(x["status"]="unknown",x,state["topics"]))

first_topic (The first topic to pick a question on):
    unknown_topics[floor(len(unknown_topics)/2)]["name"]

first_question (The first question to show the student):
    random(topics[first_topic]["questions"])

get_dependents (An expression which gets the topics to update after answering a question):
    expression("""
        [target] + flatten(map(eval(get_dependents,["target":t,"correct":correct]),t,topics[target][if(correct,"depends_on","leads_to")]))
    """)

correct (Did the student get the current question right?):
    current_question["credit"]=1

after_answering (Update the state after the student answers a question):
    let(
        ntopics, eval(get_dependents,["target":current_topic,"correct":correct])
    ,   nstate, state + ['topics': map(
                    if(tstate["topic"]["name"] in ntopics, tstate + ["status":if(correct,"passed","failed")], tstate),
                    tstate,
                    state["topics"]
                )]
    , nstate
    )

action_retry (Use up one retry and visit the same topic again):
    [
        "label": translate("diagnostic.use retry"),
        "state": state + ["retries": state["retries"]-1],
        "next_question": random(topics[current_topic]["questions"])
    ]

action_stop (Stop the exam):
    [
        "label": translate("diagnostic.end test"),
        "state": state,
        "next_question": nothing
    ]

action_move_on (Move to the next topic, or end the exam if there are no more):
    let(
        state, after_answering,
        immediate_next_topics, topics[current_topic][if(correct, "leads_to", "depends_on")],
        unknown_topics, map(x["topic"],x,filter(x["status"]="unknown",x,state["topics"])),
        unknown_immediate_topics, filter(x["name"] in immediate_next_topics,x,unknown_topics),
        next_topics, if(len(unknown_immediate_topics), unknown_immediate_topics, unknown_topics),
        finished, len(next_topics)=0 or state["finished"],
        topic,
            if(not finished,
                next_topics[floor(len(next_topics)/2)]["name"]
            ,
                nothing
            ),
        [
            "label": translate("diagnostic.move to next topic"),
            "state": after_answering,
            "next_question": if(not finished, random(topics[topic]["questions"]), nothing)
        ]
    )

can_move_on:
    action_move_on["next_question"]<>nothing

next_actions (Actions to offer to the student when they ask to move on):
    let(
        feedback, retries_feedback+"\n\n"+translate("diagnostic.next step question")
    ,   [
            "feedback": feedback,
            "actions": if(not correct and state["retries"]>0, [action_retry], []) + if(can_move_on,[action_move_on],[action_stop])
        ]
    )

after_exam_ended (Update the state after the exam ends):
    let(
        state, after_answering,
        ntopics, map(t+["status": if(t["status"]="unknown","failed",t["status"])],t,state["topics"]),
        state+["finished": true]
    )

finished (Is the test finished? True if there are no unknown topics):
    len(unknown_topics)=0 or state["finished"]

total_progress:
    let(
        num_topics, len(state["topics"]),
        known, filter(tstate["status"]<>"unknown",tstate,state["topics"]),
        passed, filter(tstate["status"]="passed",tstate,known),
        num_known, len(known),
        num_passed, len(passed),
        [
            "name": translate("control.total"),
            "progress": if(num_topics>0,num_known/num_topics,0), 
            "credit": if(num_known>0,num_passed/num_topics,0)
        ]
    )

learning_objective_progress:
    map(
        let(
            tstates, map(state["topics"][j],j,topics_by_objective[lo["name"]]),
            known, filter(tstate["status"]<>"unknown",tstate,tstates),
            passed, filter(tstate["status"]="passed",tstate,known),
            num_topics, len(tstates),
            num_known, len(known),
            num_passed, len(passed),
            ["name": lo["name"], "progress": if(num_topics>0,num_known/num_topics,0), "credit": if(finished,num_passed/num_topics,if(num_known>0,num_passed/num_known,0))]
        ),
        lo,
        learning_objectives
    )

progress (Progress on each of the learning objectives, plus total progress):
    learning_objective_progress+
    total_progress

retries_feedback:
    translate("diagnostic.now assessing topic", ["current_topic": current_topic]) + " " +
    let(
        retries, state["retries"], 
        pluralise(retries, translate("diagnostic.one retry left"), translate("diagnostic.retries left", ["retries": retries ]))
    )
    + " " +
    let(
        p,total_progress["progress"],
        percentage, dpformat(100p, 0),
        translate("diagnostic.percentage completed", ["percentage": percentage])
    )

weak_objective_threshold (The amount of credit below which a learning objective is considered weak):
    0.6

finished_feedback:
    let(
        weak_objectives, filter(p["credit"]<weak_objective_threshold, p, learning_objective_progress),
    //
        translate("diagnostic.test is over") + " "
        +
        if(len(weak_objectives)=0,
            translate("diagnostic.passed all lo")
        ,
            translate("diagnostic.more work on lo", ["los": 
                join(map(lo["name"], lo, weak_objectives),", ")])
        )
    )

feedback:
    if(finished,
        finished_feedback,
        retries_feedback
    )

Custom diagnostic algorithm

Interface theme

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Interface language

Allow students to print question content?

Show student's name?

Enter review mode immediately on ending the exam?

	Always	In submitted mode	Only in review mode	Never
Show answer correctness
Show the student's score
Show the maximum score
Show part feedback messages
Show expected answers
Show question advice

Pass threshold

Feedback messages

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Paul's copy of Blathnaid's copy of Blathnaid's copy of Complex numbers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Paul Molloy 6 years, 4 months ago

Question groups

Topics

Learning objectives

Base diagnostic algorithm

Custom diagnostic algorithm

On leaving a question

On timeout

5 minutes before timeout