Access VBA: SQL query causes UPDATE syntax error

I have a database with linked tables- Staff, Courses and Training_Record. Each staff member has a numeric primary key, as does each course and each entry in the Training_Record table. The Staff_ID and Course_ID in the Training_Record reference records in Staff and Courses.

When a staff member or course is added, the Training_Record (fields: Staff_ID, Course_ID, Date_Taken, Notes) has staff,course records inserted- so adding staff member 1 would insert records (1,1,,,), (1,2,,,) etc, adding course 8 would insert records (1,8,,,), (2,8,,,) and so on. This works.

I then have a form to record training. The user selects the course, enters the date and selects staff members from a listbox. I have a save button which triggers VBA code. The date and course are pulled from the boxes and I loop round the listbox, concatenating selected staff members into a string. This all works and a message box displays, verifying that. Then, an update SQL query should be run, updating the Training_Record.

The problem I have is with the SQL update. I have an update query that will work in the SQL query editor, though it uses written in variables:

UPDATE Training_Record
SET Date_Taken = '12/12/12'
WHERE Staff_ID IN (1,2,3,4,5) AND Course_ID = 4

This updates the Training_Record to show that staff 1,2,3,4 and 5 took course 4 on 12/12/12. However, in VBA this will not work. This is my SQL query in VBA:

strSQL = "UPDATE Training_Record" _
       & "SET Date_Taken = (" & strDate & ")" _
       & "WHERE Staff_ID IN (" & strCriteria & ") AND Course_ID = (" & strCourse & ")"

DoCmd.RunSQL strSQL

The error that the code generates is "Run-time error '3144': Syntax error in UPDATE statement." and the debugger highlights the DoCmd.RunSQL statement following the query.The entire VBA code:

Private Sub SaveTraining_Click()

Dim db As DAO.Database
Dim VarItem As Variant
Dim strCriteria As String
Dim strDate As Variant
Dim strCourse As Variant
Dim strSQL As String

Set db = CurrentDb()

'Extract the course ID and the training date from the form
strCourse = Me!CourseID.Value
strDate = Me!TrainingDate.Value

'Dealing with empty boxes- zero length
If IsNull(strCourse) Then
    MsgBox "Please select a course." _
        , vbOKOnly, "No course selected"
End If

If IsNull(strDate) Then
    MsgBox "Please enter a date." _
        , vbOKOnly, "No date given"
End If

If StaffMembers.ItemsSelected.Count = 0 Then
    MsgBox "Please select staff members." _
        , vbOKOnly, "No staff members"
End If

If (Not IsNull(strCourse)) And (Not IsNull(strDate)) And (StaffMembers.ItemsSelected.Count > 0) Then

    'Extract each selected member and concatenate into a string for sql query

    For Each VarItem In Me!StaffMembers.ItemsSelected
        strCriteria = strCriteria & "," & Me!StaffMembers.ItemData(VarItem)
    Next VarItem

    'Gets rid of extra comma on query string
    strCriteria = Right(strCriteria, Len(strCriteria) - 1)

    'Message box
    MsgBox ("Staff: " & strCriteria & vbNewLine & "Date: " & strDate & vbNewLine & "Course: " & strCourse & vbNewLine & "No. Selected staff: " & StaffMembers.ItemsSelected.Count)

    strSQL = "UPDATE Training_Record" _
           & "SET Date_Taken = (" & strDate & ")" _
           & "WHERE Staff_ID IN (" & strCriteria & ") AND Course_ID = (" & strCourse & ")"

    DoCmd.RunSQL strSQL

End If

Set db = Nothing

End Sub

TL;DR I can't make a SQL UPDATE query run in VBA

I've got a feeling that it's an error in syntax somewhere, but I can't find where. Any ideas/advice would be much appreciated, thanks.