RShiny: checkboxInput numeric conversion not working in scoring methodology

I'm wanting to use checkboxInput to indicate which variables need to go into a scoring methodology (i.e., have the ability to leave some variables out if desired). I want the checkboxInput to be converted to a 0 or 1, and this number will be used in a scoring algorithm.

I know the scoring methodology is working because it will work when I have default variables chosen which ignore the checkboxInput, but not with these manual check boxes.

I'd greatly appreciate any help. Below isn't an exact replica of code; just a simplified version to make this easier for readers. If this way too simplified, let me know; the actual code is pretty complicated but I want to highlight the simple issue that's causing me such a headache for an unknown reason. Thank you!

I've tried making the checkboxInput a reactive variable(s), I've turned them into integers, etc. I feel like there's something obvious I'm missing.

Here is the code:

ui:

    (
        uiOutput('variable1selected'),  
        uiOutput('variable2selected'), 
        uiOutput("variable3selected")
    )

server:

    output$variable1selected = renderUI({
        checkboxInput("variable1selected",
            "Include Variable 1 in Analysis",
             value=TRUE)
    })
    output$variable2selected = renderUI({
        checkboxInput("variable2selected",
            "Include Variable 2 in Analysis",
            value=TRUE)
    })
    output$variable3selected = renderUI({
        checkboxInput("variable3selected",
        "Include Variable 3 in Analysis",
        value=TRUE)
    })

    variable1selected = reactive({as.integer(input$variable1selected)})
    variable2selected = reactive({as.integer(input$variable2selected)})
    variable3selected = reactive({as.integer(input$variable3selected)})

    Score = variable1selected()*10 + variable2selected()*20 + 
        variable3selected()*30

There aren't any error messages, it's just not scoring at all when the checkboxInput is selected. I'm expecting a score for each row, and then I sort the table by that score. What's actually being produced is an unsorted table because there is no score present to sort (the "Score" variable is NA for each row).